WARNING: lots of spoilers about āThe Secret of Monkey Islandā and āMonkey Island 2: LeChuckās Revengeā, below.
Iāll try to explain why I think MI2 is a better game but I also consider MI1 my favorite adventure game. Maybe writing down these thoughts will help me to understand if my preference is mainly based on nostalgia or not.
First, the higher production values of MI2 are evident and, personally, had a very positive effect on me.
Graphics
While I love the graphics of MI1 backgrounds, playing MI2 was like living in a painting. When I saw for the first time the scanned backgrounds of MI2 I was flabbergasted. I donāt think that pixel-art backgrounds are intrinsically worse or better than backgrounds created with other methodologies: regardless of the method used, the important thing to me is if the final graphics manage to convey the right atmosphere. MI2 was (and still is) an adventure game with one of the most beautiful graphics ever and to me it was clear from the first moment that scanning hand-drawn pictures moved the quality on a new level.
(Scabb island cemetery. Design by Steve Purcell. Drawn by Peter Chan)
Atmosphere and mood
One of the things that both MI1 and MI2 do right is to put the player in a dreamy atmosphere when the game starts and this goal is accomplished in part by the fact that itās night both on Melee island and on Scabb island. Walking on Melee and visiting all its darkest places really captivated me and Iāll never forget that magical feeling that I felt moving Guybrush on the Melee map or walking in the woods.
MI2 had also these moments and to me the most memorable of them was when I visited for the first time the cemetery on Scabb island: the iMUSE system smoothly provided a slow and gentle music to highlight the sadness and solemnity of the place. I was quite impressed when I experienced it the first time.
If there is one thing that MI1 did better than MI2 in this context is in my opinion the fact that it used in an intelligent way the lack of background music in some places. When I walked on the Melee docks, I was surrounded by silence and that helped me to feel that it was night, when most people sleepā¦ until I entered the SCUMM bar and was invested by a cheerful music that highlighted the alcoholic activities of a mass of local pirates. The music of the SCUMM bar was good but it was the sudden change between silence and music that made me feel the SCUMM bar even more lively. On the contrary, the soundtrack of MI2 was quite pervasive and I canāt remember of a context or location in which silence was used in a similar way.
Music
Itās difficult for me to choose between the soundtrack of MI1 and the soundtrack of MI2. Despite having played the two games about the same quantity of times, I remember more easily the music of MI1 which, by definition, I should consider more memorable to me. 
I think that the score of MI1 has more ācatchyā tunes and thatās probably why I remember them more easily. Some of the songs of MI2 are variations of the same melody or at least recreate a very similar atmosphere (the track of Elaineās Mardi Gras party and the track played when Guybrush is chased by the cook are very similar; the Scabb swamp and the graveyard have musics that are quite similar in style). It needs to be specified, however, that the fact that MI2 provides also some variations of the same melody shouldnāt be interpreted as a lack of original new tunes; on the contrary! MI2 is full of good new music: I have already cited the music of the graveyard as one of those that impressed me the most, but the Largo theme is also great.
I would say that the music of MI2 is globally composed and arranged in a more sophisticated way when compared to MI1, but thatās just my uneducated impression. The decision of arranging the well known main themes sometimes produced results that I like less, for example I like more the original opening theme of MI1. Other times some themes were used more effectively in MI2, like the LeChuck theme briefly cited before sending you into A Dimension of Infinite Painā¢ (which, BTW, is still one of the most scariest moments I have experienced in any game). And letās not forget that one of the songs of MI2 was also used for a puzzle!
Overall, I would say that I consider the soundtrack of MI2 of higher quality from an artistic point of view, but itās more probable that I would hum under the shower an original tune of MI1.
Puzzles
Puzzles in MI1 were good and some of them are my favorite puzzles of the series. I have already cited the āgrog puzzleā as my favorite one, but there are also other special puzzles, like the insult fight (which in my opinion is interesting more because of the funny insults than because of the puzzle to solve).
But thatās just about single specific puzzles, not about entire puzzle chains. When it comes to puzzle chains it seems to me that MI2 takes the cake: searching for the four pieces of the map is IMHO the best succession of events and puzzles ever created for an adventure game and this goal is accomplished in part by the fact that I perceived the second chapter of MI2 as enormous. When, after a long succession of events and activities, I finally used the fishing pole on Booty island to retrieve a piece of map from a cliff and I was 100% sure that the little evading piece ofā¦ paper was finally mine, but it wasnāt! Something suddenly happened and I realized that the exhausting chase was not over yet! I still remember what I thought back then: āMy god, this game/puzzle never ends!ā.
The three trials in MI1 are good, but collecting the pieces of map in MI2 is the most intriguing, creative, rich and well designed sequence of events that I have played in an adventure game. Here MI2 wins hands down.
Since Iām talking about puzzles, letās make clear that both MI2 and MI1 had flaws: in MI2 there is the infamous monkey wrench puzzle and in MI1 there is the āred herringā puzzle, that for a non-English player like me was equally incomprehensible.
I also like the cleverness of some puzzles in MI2. For example, Guybrush has to realize that he has to create e voodoo doll for Lechuck following the same recipe that the voodoo Lady taught him for Largo. The āIf this is 3, what is this?ā was also a small but quite smart puzzle, in my opinion.
Story
I have not observed a strong similarity between the stories of MI1 and MI2, if we exclude that the protagonist and the main villain have to confront each other again. In MI2 your goal is to find a treasure and you have to escape from an island, find a map, following its directions andā¦ being catapulted into a place completely unrelated to pirates of the Caribbean, but maybe related to āPirates of the Caribbeanā¢ā.
Actually, I think that the story of MI2 is not just profoundly different from the one of MI1 but also that MI2 was the first chapter of the series in which the authors started to give stronger hints aboutā¦ āthe wider perspectiveā of the story. MI1 was just an introduction to the world of Guybrush: the player notices some funny anachronism but itās easy to assume that they were put there just for comedy purposes, but in MI2 the story becomes more complex: not only the quantity of anachronisms increases but they start to seem somewhat related to each other. Why on earth there are the same tunnels under several islands (under Dinky island, under Phatt island, and even under Melee!)? What are all these shenanigans about theme parks and tickets? What has this to do with pirates? Wasnāt the player supposed to find a treasure? Did Guybrush find it? And what about the controversial and puzzling ending (that I perceived as a cliffhanger)?
It seems to me that the story of MI2 drastically deviates from the more simple story of MI1, which in retrospect seems just a fantasy fable for kids. Is MI2 still a story about pirates or does it reveal a different reality? All these question have never been answered in an official way and regardless of how much you like MI2 and its ending, my point is that its story is completely a different beast from the one shown in MI1.
Design
I know almost nothing about game design, so Iāll be brief: both games seem quite well designed to me but I HATE the fact that in MI1 you can progress without even meeting the Voodoo Lady. It happened to me the first time that I played the game, which I finished without ever meeting the character! When eventually I realized that there was a completely unknown character that I never met, I was traumatized by the discovery. The Voodoo Lady is a fascinating character that provides a backstory that makes that fantasy world more alive. She also helps the player to understand better whatās happening. Spending time, money and efforts to design and create such a useful character and then making her completely optional is in my opinion a design flaw.
My personal conclusions
So, what are my feelings after having written this wall of text? I still think that MI2 is, technically, a better game. Actually, writing down these thoughts and collecting all these memories has made me realize that I like this game even more than I believed. 
The game is richer, more complex, has clever and long puzzle chains and provides a story that is more sophisticated and mysterious than the one written for MI1.
MI1 is a good game and since it was the first adventure game that I really liked it will always be my favorite one, but I still think that MI2 should take the trophy.
).
