Yesterday I finished Mass Effect 1, every single mission completed except for one (Scan the Keepers, I was missing two, and didn't feel like tracking down which ones I missed). This includes all the DLC missions.
Overall, GREATLY improved from a combat perspective. It made starting ME2 less jarring because the interface from ME2 was moved back into ME1. Combat *IS* easier now in ME1 because of the balance changes. Biotic cooldowns and such are all much faster now, and any class can use any weapon. You still only get buffs for class specific weapons. But I was able to rock an Assault Rifle and a Sniper Rifle on my Vanguard when being in shotgun range wasn't an option. The AI for your team members is a bit better than it was, but they will still often stand in front of you blocking your fire. The AI for the enemy has slightly better pathing it seems, but there was this weird issue where they would pop out from cover, and then instantly vanish back behind cover, and then pop out again. It was kind of jarring to see.
Visuals were so much better, though not perfect, there was still some engine limitations.
I didn't have any missions get stuck in some weird state, which was semi common in the original.
Overall, I would be hard pressed to ever want to play the original version of the game for the combat issues it had, much less all the other nice to haves that LE introduces.