I must admit that my opinion is heavily biased because DA2 was the first dragon age and the first Xbox 360 game i ever played. I played it like this: DA2-DA:O-DA:I
All the games were very different, i am not too sure how do describe it but they have all changed in major ways.
DA:O had a solid story and good cast but it felt very rushed and quite stereotypical, 4 main quests which mostly involved fantasy stereotypes such as elves who live in the forest or elves that are servants and lower class to humans, Dwarves who lived underground and had a major fascination with money etc...
I am a completionist in every way but to be honest i only did a few side quests here and there, why did i have help someone steal from nobles? did it help my cause? no it did not.
Overall i liked DA:O, i have completed it twice and that is probably all i will.
DA2 has a believable story and a amazing cast but it reused areas and it was basically only there to serve as something to lead up to inquisition.
Most characters in this game can be summed up with two words: A survivor, This i could relate to, not because i have overcome anything bad or terrible but because it is realistic in most ways. Your town gets destroyed? protect your family, A family member dies? you grieve,move on and help the remaining ones, You have to work your ass of just to live in a shitty house? you do it to put a roof over your family's head.
I liked every character even though most had traits i do not like, they all just had something about them like Isabella, she was more of a flirt than Varric and i did not like that at first but learning about her motives and feelings i really grew to like her .
( i wish that they added a achievement for doing every side quest, because i did ;D )
I have completed the game four times.
I can't say too much about DA:I as i have not got too far into it, i accidentally spent 20 hours in the Hinterlands but i do not feel very engaged with the characters.
The romance is amazing it has obviously been the best so far but i find myself not really caring about the characters themselves and more about if they are my friend etc..
I enjoy the combat although i must admit i have not used tactical camera yet. (i doubt i will)
I love all of the dialogue options and perks as i think that was a really big improvement, i miss the dominant tone thing though.
I think in the end i like inquisition more than origins but less than DA2, i do not feel that the inquisitor is fleshed out as the previous protagonists.
In the end i like that all games are extremely different and have a different protagonist, each character gives a unique quality to the game and they really do make you feel special in each game however as much as i would like to see some companions again i hope they do not bring anyone back in the next DA, Hawke and Varric did not work out in this game so i think it makes it pretty clear that reviving characters is not something worth doing next time.
(sorry for rambling or not making sense, writing at 4am is not something i will attempt again
)