All three games have their strong points that the others aren't quite up to snuff.
1 excels in setting, and grand scale story telling. It's the kinda of story that feels more like something out of an epoch of a book series than just a game. The Character strength is there and fleshed out, but some of them fall flat as no one was certain at the time that it'd sell well enough to make a sequel, and so a few corners were cut to reinforce the more obvious and easily reached points of the game. The combat's use of an overheat system means you will NEVER run out of ammo, but careless use of your weapons will leave you in a jam for a short period. one that could be disastrous. the Ability to apply modded ammo was a huge boon if you had a good variety to choose from, making any weapon viable against any threat with a single trip to the menu. This game has two major DLC's though only one is of particular interest for carry over saves. Both are worth having though.
2 Excels in character driven story, and both succeeds and fails at making improvements to combat. It's more mobile than 1's, and the variety of guns do feel more defined from each other than in 1, were an AR was an AR regardless of stats. However, the introduction of limited ammo and shared cool down for powers/abilities is a REAL issue with a lot of fans of 1's combat, like myself. The introduction of Ammo effects as Powers eliminates the RNG factor for ammo types the last game relied upon, but then make your ammo options limited and defined by who you have with you. This game's plot DLC's all play well into the next game, as well as stand alones that they are. Truly worth the investment in all the DLC's.
3 .... 3 is something... If you are like many players before you, and you get attached to the lore and whats actually going on, and what happens to characters? Then this game is going to be hitting you in the gut, repeatedly. Especially if you're a paragon player. In a good way. Combat is further refined, and the guns even more varied feeling, making weapon choices even more important beyond what gun hurts most. Lore wise though, while 2 kinda starts bending it's own lore, 3 kinda takes lore around how biotics and mass effect fields work, and just pretty much breaks it over it's knee and just uses "Biotics" As "space magic" which while leading to fun and enjoyable powers, is something a sour note for those of us who loved 1's fairly hard science based lore. The Multiplayer actually plays well, though you may feel a bit overwhelmed till you adjust to the difference between single and multi player modes.
that said, 3 is a fantastic game, wonderful and well made, up until the final act. The final assault on Earth plays well, but once you get blasted and start, what we now call, " the slow march" the game kinda just sinks right into the toilet, but *shrug* Their ALL worth playing, and the DLC's as well.