I played Escape from MI (which I am assuming is kiiiinda similar to Secret of MI) and Grim Fandango. Loved both.

* possible spoiler alert *

Both are puzzle kind of games. There isn't anything like the insult fighting in GF. Both storylines are fascinating and suck you right in. Great voice acting and sidekicks. I think (if I recall correctly) both games make you travel to different places.

I found that GF moved me a lot more emotionally than MI (subjective, yeah) and I think it's probably because the GF storyline is a little darker/serious (not to say it didn't have funny moments). When I finished MI, I felt accomplished. When I felt GF, I felt like I was saying goodbye to friends that I'm not sure I would ever see again. That kind of feeling.

I could go on and on, but I don't want to spoil it too much more. :)