2 doesn't do anything better in the gameplay department. Rushing is worse, cover was pretty similar (maybe a bit improved in 3), sniping wasn't as good (though it improved on 1). And the RPG elements are really dumbed down for some reason. It's a pity because the gameplay's certainly better than 1, but 3 takes the best of both and refines them for a better overall experience.
It's been a while since I played both games, so I might have some things wrong, but I'll write the things I remember. I also never played the MP in ME3, just FYI.
In ME2, all enemies have additional layers of protection on Insanity and the one difficulty setting below that. This has a significant impact on how you play the game, and I actually think the game on lower difficulty settings is much worse. When for example Husks don't have any armor, they're completely trivial (even in large groups) as you can just lift them with bionics and you're done. The same thing is true in ME3. It has a pretty large effect on most basic enemies; it forces you to play more strategically and it makes picking the right powers and squad members a lot more important. You can't just do biotic explosions on everyone from the get go.
Another change I don't like is the cool down system. I get that a lot of people probably think the equip load vs cool down system is a good addition, but if you minimize the cool downs they're simply too short. I forget the exact number, but as an Adept I think you can cast the quick powers like Throw with cool downs less than 2 seconds. I don't like it because it made playing an Adept (my preferred class) turn into nothing but spamming powers. In ME2 the powers have long cool downs. Maybe some people think they're too long, but it means that you a) have to be more considerate in how you use them b) have to use your guns as well. ME2 introduced an ammo system, and I found myself actually going around looking for ammo, changing weapons during combat because of ammo etc. That never happened in ME3, I used my gun so sparingly it was never an issue. Maybe not the case if you play a Soldier, but why play a Soldier heh. Being able to spam powers that rapidly simply wasn't enjoyable for me, but I did it because it seemed like the most effective way to play.
The third thing I don't like is the encounter design, and the enemy design / variety. ME2 had a butt load of different enemy types. They would be too many to list here, but it was basically every race in the game, spread across at least five different factions. I'll concede that the differences between them were to some extent superficial, but in a 40 hour RPG variety is nice. You know you only ever fight the Collectors on three missions in ME2, and that makes each time feel kind of special.
ME3 has two main enemy factions (Cerberus and Reapers), with some Geth every now and then. Not only is there less variety off the bat (no Vorcha, no Batarians, no Krogans etc. not even any of those fun but easy mechs), but I straight up like all the enemy designs way less. I don't like how the Cerberus troops look and I don't like how they sound, and I don't like fighting them. I don't like the riot shield guys, I don't like the shield generators and I don't like the turrets. This sounds stupid, but I even think the bipedal mechs look way worse than the robot ones in ME2.
The Reapers are slightly better I suppose, they did try to give them some diversity, but again as a matter of personal taste I just don't like them as enemies. Their designs simply don't appeal to me in the least. As for the encounter design, there are a lot of them where you're expected to run around constantly, because enemies keep coming and you'll get flanked if you don't. You say the rushing is better, which might be true, but it's not good. I don't think these types of encounters work well at all together with the game systems they designed. Which isn't to say that I think you should be able to go through every combat encounter without moving, I don't think you should and that wasn't the case in ME2, but I don't think the extent to which you have to run around in ME3 is good.
Then there's small shit like how I think all the weapons in ME3 sound weak as hell, even the ones I like from ME2. Or how the customisation system people were so happy to have is kinda lame because the weapon upgrades aren't all that interesting.
It's just personal taste in the end. I like ME2's combat pace much more than ME3's, which I think feels less strategic, and the fact that I hardly enjoy any of the enemy designs in the game makes the game so much more of a chore to play. I kept replaying ME2 just for the combat, whereas in ME3 I never got to the point of even enjoying it.