Intro
ME2 is just the better game - by far, if you ask me. It's for plenty of reasons. I'm gonna make this long-winded. Yes - explanation incoming.
Combat
ME1's weakness was that its combat was quite clunky - like most RPG/Shooter games. ME2 basically removed all of the clunky-ness by...reversing things and making it go the Shooter/RPG route. It basically went the other way around. ME is a series that always felt like a shooter series b/c of its controls - so, it made sense to me w/ the removal of the Inventory system and being way less stat-driven. Plus, this immediacy makes the player also be more invested into the actual game and combat than in spending time in the game's Inventory system.
Inventory, Loot, and Planet Scanning
Let's face it - ME1's Inventory system and loot system was not good at all. While I did like that I could add in extra mods and stuff to weapons - the weapon naming was silly for most of the weapons. Most guns were like version 1, 2, 3, 4, etc. And going through that Inventory was almost silly - b/c most weapons weren't much different than its previous numbered incarnation - maybe it got a few more damage points and a one more mod spot to tweak-out w/ each gun, but that's really it.
The upgrading system in ME2 simplified the above. Basically, now you got a handful of weapons and guns - and that's it. And well - you want to upgrade them to some kind of extent, then you're gonna have to find resources and/or especially do the planet scanning. Advice on planet scanning - don't do too much of it in a row b/c that can get boring and tedious. Do it here and there and you'll be fine.
Manual Flying
About manual flying in ME2 - I think they were trying to be different from ME1 and Dragon Age: Origins - where in those games, you just click somewhere and it just basically goes there. ME2 goes another route and it makes you feel like you are flying around in this huge-as-sin universe in outer-space. It also makes you feel that shouldn't waste your money and resources when always flying around and that you should wisely go around the world. As far as I'm concerned - different is always a good thing. I don't need each game to be just like each other.
Questing & Story
While the main quest was really good in ME1, the side quests stuff....was kinda "meh," for the most part. This is especially true, when ME1 is compared to ME2's side quests and Loyalty Quests. Now, most of ME2 is based around building your squad. And you will want to do Loyalty missions, as well - b/c of the extra skill perk and b/c these missions are great. All of these missions about your characters actually will make you care about them. And you'll care even more about your characters, especially when the final mission in ME2 rolls around - b/c every squad member's life in this "suicide mission" actually hangs in the balance. There's more of an emphasis on saving your squad than actually saving the world here (even though both storylines are here) - b/c of the huge emphasis really put forth on the squad.
A lot of ME2 feels more linear in design, as many of these planets are not "Hubs" - "Hubs" would be like the planet in ME2 where Club Afterlife is at or ME1's The Citadel. Most of these "planets" in ME2 are just there as linear-style Call of Duty missions. Unlike a COD game, though - these linear-style missions often have decisions to make that will matters and have ramifications. If I had one complaint w/ ME2 and its questing - I just wish there were more "Hub" style locations/planets in the game.
EDIT:
MysterD's Complaints w/ ME2
So, what are my complaints w/ ME2? Well, I wish there more "Hub" locations; the planet-scanning had more depth and variety to it; and upgrading my few weapons on the Normandy was deeper than it actually was.
That's basically it. All VERY minor stuff.