Having just played both Dragon Age: Origins (Ultimate Edition which came with the Awakening expansion pack and other DLCs) and Dragon Age 2 I thought I'd provide some of my thoughts of the first game compared to the sequel.
Both games were the first RPGs I've experienced that had very realistic voice acting and realistic facial animations. Being an RPG fan dating from the SSI "Goldbox" AD&D games in the 90s, "Eye of the Beholder" and others great ones such as Icewind Dale, IWD2, Baldur's Gate, BG2, the Dragon Age games certainly gave the best NPG/Companion character interaction experiences. The aid of new 3D technology certainly helped and the terrific voice acting was very impressive.
Dragon Age 2, in parts, gave me a sense that the Bioware didn't spend as much time as it wanted to to fine tune/enhance the game. Many of the dungeons felt recycled- it's like er, haven't I been here before? Dungeon design-wise DA2 was a huge step backwards vs Dragon Age. Same with the variety of creatures/monsters. I felt like I was fighting slavers and abdominations all the time, and many of which look pretty much the same as the ones from Origins. All of the above were big negatives for DA2. The story itself also seem to take the easy way out in terms of resolution by pretty much have everyone die/go crazy. Perfect examples- Merrill's mirror image quest and of course the "Final Straw" main storyline quest.
In terms of "traveling", I did not get the sense of the size of the "world" I got in Dragon Age in DA2. There's not really a "world map"- just some icons designating locations. So in that sense you feel kind of "trapped" in Kirkwall and its surroundings. Origins was certainly more "epic" than DA2.
I also missed the camp from Dragon Age I where you got to interact with your companions centrally. In DA2 you had to travel to the companion's "home" to strike up conversations. That was not a huge issue though.
I read about how people complained about how Dragon Age 2 is too action-centric and became too much of a real-time RPG. After playing it I cannot agree. I found myself pausing during most combats to evaluate the current situation. Perhaps it's because I played as a mage and with more abilities/spells available I didn't see it as too much of a real-time game as others.
But I preferred the combat in Dragon Age Origins better. What I first began DA2 in that first fight I was like WTF, I can't zoom out all the way! So hopefully in Dragon Age 3 Bioware will bring back the "tactical" combat view. From the sounds of things Bioware is going to make positioning your party members important again in DA3 so that's something nice to look forward to for us classic RPG fans who value strategy. In Dragon Age 2 you can cast fireball spells on yourself all the time and not get you nor your companions hurt. Not very realistic (but necessary in DA2 to survive).
Minor features added in Dragon Age 2 were nice. I liked how I was able turn on the experience (XP) display so that you know how much you gained after a battle and completing a quest. Also I did appreciate how Dragon Age 2 had quest locations and important people to talk to highlighted so I didn't have to waste time bumbling around. It was also nice that crap inventory items were grouped as "junk" and easily sold with one click.
As for the Holy Sh*t and OMG moments in both games- Origins beats out DA2. First such moment in Origins- the recruit getting killed by Duncan, then it was the death of the King. And of course the romance scenes with Morrigan. The only one I could remember in Dragon Age 2 was when mother was killed by a psycho mage, and that was more of a WTF moment.
Boss fights-wise, the toughest ones in Dragon Age 1 were vs Ser Cauthrien and her posse and also that crazy Harvest Monster in Golems of Amgarrak DLC. Neither one of which I was able to defeat. Seems that the Harvester monster was also shamelessly used in DA2 in the form that First Enchanter Orsino took near the end of the game. That was confusing/difficult to believe that Orsino would resort that that, but I digress- it was probably again because the game was rushed. In DA2- toughest battle for me was the High Dragon in the Bone Pit. The final battles were relatively easy because all your companions were fighting alongside you.
Overall though I enjoyed BOTH games immensely. Obviously, Dragon Age appealed more to the classic RPG fans such as myself more, but I also enjoyed many of the improvements in DA2 over Dragon Age. That said I very much look forward to Dragon Age 3 which is already in the works