On the subject of Roxas's characterization, Hirokey did a great job of identifying where and why he differs between games. To add to that a bit: Roxas's character can be interpreted as the marriage of two key qualities-- naivety and idealism. His naivety is a product of his circumstances and it informs his behavior in both Days and KH2. His idealism is a deliberate echo of Sora's: it is in so many words the sum of his parts, from his brash, emotionally pronounced confrontational side to his fanciful and cautiously curious personality, and it manifests not just as a result of his circumstances but in the nature of his circumstances themselves. In Days, Roxas lives out an almost effortless, routine existence made up of ice cream and friendly banter; in KH2, he is literally walking about an artificially crafted Twilight Town designed as his ideal landscape-- but in both scenarios, Roxas is also a prisoner, trapped by forces larger than himself and unequipped with even rudimentary knowledge as to the reality of his situation. And we see, in both games, exactly what Roxas does when he gains access to reality and where his idealism contrasts with that of Sora: Roxas, by virtue of his naivety, assigns a nostalgic facade to friendship and uses routine, exclusive pleasures as a protective measure against the encroachment of the "outside" world. Sora, on the other hand, sees the bigger picture and undertakes his friendships and connections with others as a manner of actively accessing a larger vision of community: where Roxas sees a closed loop and is prone to mistrusting people who don't fit into his neat and tidy circle, Sora accepts people as they are (even the bad guys).
This is why we see Roxas, in Days, pushing back against Axel during the latter portion of the game: Axel broke the simple vision of friendship Roxas had been conditioning himself to cling to by withholding information; it's likewise why we see Roxas lash out so fiercely towards the end of his prologue in KH2 (Hirokey alluded to this), as he realizes his ideal has been irreparably shattered and can't bring himself to accept that-- even though he himself was complicit in both instances, asking questions he didn't really want answered. There's the scene in Days where he murmurs to himself on the clock tower after abandoning the Organization, "Where did I think I could go?" It's a tonal mirror of his resignation in KH2, when he realizes he can't escape the inevitable and that, indeed, his summer vacation is over. The stubbornness of his convictions and his unwillingness to relinquish himself to fate are central traits of Roxas as a character which carry from KH2 to Days and back again.
I think encountering Days with the understanding that it's actively investigating this dualistic, self-empowered/self-defeating element of Roxas puts things into perspective. It's not arbitrary: Days encourages these meta-readings of its characters (after all, everything about Roxas is dual in nature, whether he's being cast against Xion or Sora or literally fighting with two keys) and internal dynamics, but we can also understand Roxas in the narrative context, as someone whose spirit is molded in the midst of the duplicitous Organization and singularly manipulative entities like Xemnas, Xigbar and Saix. Of course he's an idealist: having nothing of reliable substance to measure his concepts of others against, we see him grasp at the only genuine connection he makes with Xion and Axel, and covet it, like when he suggests that everything should stay exactly the same forever (impossible but sweet) or when he encourages the two of them to run away with him (decidedly not a solution, also sweet). So it makes sense that in KH2, he would invoke the names of Hayner, Pence and Olette as a sort of talisman when his ideal comes under threat, and why, after that fails to fend off reality, he surrenders to Namine and asks her to outline how it all ends for him because "nothing else matters anymore." (Of course, DiZ has to foil that budding relationship because he's obsessed with playing both god and devil's advocate to the Organization's thesis, but then AtW is a whole other can of worms.)
