The first one was the best as it embraced that sense of exploring the galaxy, meeting new people and races and being part of a greater galactic society. People and races had enough unique character and charm to feel decidly different and the atmosphere/tone of the game was genuinely immersive. It's only when everything becomes about the "impending doom" that any really diversity and flavour starts to die. Speaking of which...
ME2 was stripped down in many regards and "streamlined" for endless corridor gunfights (I totally loved the Kasumi mission). It did have Omega though, and that place was great. Also, it has several of my favourite ME characters in it. For the record, no, I do not like Mordin, and well... I didn't care (No spoilers).
ME3 is a bit better with the RPG and customisation stuff, but still manages to fall short. It's pretty linear, the dialogue appears a bit underdeveloped in places, and the ending was a bit lacking (though I enjoyed the choice I made). What more, you HAVE to play the Multiplayer! I mean, the MP isn't that bad tbh, but you have to play it if you want the best ending. Unfortunately, the Multiplayer is confirmed as returning for Andromeda too, so, that doesn't instill me with hope.
Overall, it's an incredible series that sets the bar high, but doesn't ever really fulfill that Star Trek captain roleplay after about halfway through ME1.
I am immensely skeptical of Andromeda and I'll probably not be preordering it, as no-one knows what to really expect yet.