I did a quick run down from the top of my head the differences between the various Mass Effects. This isn't a complete list, but I think it boils down to two things. I enjoyed the story of Mass Effect 1 and most of 3. Combat was greatly improved overall, but ME1 combat was servicable.
For Mass Effect 1:
Run/Gun mechanics are clunky, but servicable
Hard to use biotics around cover.
Individual cooldown allowed for faster use of powers.
Hand grenades are useful.
Gun heating mechanic is awesome.
Conrad is right.
Cover mechanics are clunky and difficult to work with.
No rolls/dives.
Mako was hard to handle, but could be nimble with practice. It also helped make the worlds and galaxy feel much bigger. Removing this makes the galaxy feel smaller to me.
The story was incredible. Best writing in the Mass Effect series.
The character interaction was limited to just Shepard (unless in a mission or elevator) and was very well written.
Best villains (Saren/Sovereign).
The ending was epic and felt like the game was turned up to 11.
Ending cut scenes set the stage for ME3 perfectly while providing a good denoument.
For Mass Effect 2:
Run/Gun mechanics are much better.
Biotics curve which is a big improvement.
Universal cooldown hurt the quick use of powers.
No hand grenades unless you have a squad mate with them as a power.
Thermal clips are a step back.
Cover mechanics are much better.
No rolls/dives.
No Vehicle sections until DLC. This made the universe feel smaller.
Hammerhead was very maneuverable and easy to use.
It also had weak missiles and tissue paper armour.
The story was short and relatively weak. It suffered from being the middle child.
Character interaction was turned up to 11. You got to know each squadmate very well and make friends.
The Illusive Man was a very well written friend of convenience. Harbinger was a decent enemy, but did not match Saren/Sovereign.
The final mission was also turned to 11. Your decisions in the game are revealed here. The squadmates you got to know could die based upon your decision.
Ending cut scenes set the stage for ME3 perfectly while providing a good denoument.
Mass Effect 3:
Run/Gun mechanics feel unchanged from ME2 (very good)
Cover mechanics improved again (jumping over cover)
Controls suffer from one button for everything... reviving a squad member and accidentally taking cover can lead to death.
Rolls/Dives added and are my most used move when taking fire.
No Vehicle sections. Universe is made even smaller.
Shepard begins speaking at length without player input.
The story up until the Priority: Earth is incredible.
The story at Priority: Earth falls flat in comparison.
The story only has three 98% similar endings.
Character interaction is appropriately toned down from ME2.
Character interaction between other NPCs is incredible. Having the crew go ashore and calling/chatting with each other was a great design decision to make the world breathe more.
The Illusive Man is a great enemy. Very well done.
Harbinger is almost completely abscent and has no lines.
The Star Child is introduced late and there is no real conversation. Terrible "villian" for this story because there is no history or interaction with him.
The Reaper motivation is circular. (I would have preferred if they had left the motivation a mystery)
The final mission did not take into account the preparation done during the rest of the game.
The EMS score did not impact the effectiveness of your forces in a significant way (I would have preferred high EMS making final missions easier)
Your war assets did not come into play in a similar manner as DA:O or ME2.
Ending cut scenes do not provide any denoument.