It's been awhile since I've played Cross, so I might not be able to give it the justification and memories that some parts of it deserve, but there are two particular qualities that stand out to me that I've noticed recently.
A) I've watched the sequilitis series done by Egoraptor and I think he provides enough diplomatic language and particular gaming and design concepts I can relate to and remember between Trigger and Cross and
B) my lingering recollections of the games.
Yes Cross is not Trigger 2, and I can understand to that. However with the use of "Chrono" intentionally in its name and how its used, its intended to alert players that this is an effective 'sequal' to becoming a chrono series, even more so when each re-release of Trigger makes more 'connections' to Cross. So, the quick-call I would say about Cross is I think its an ungraceful sequel. I could probably ramble and maybe make a spiffy argument as best I am able with uses of rhetoric, but I think some of the concepts come off easily enough by looking at Trigger and Cross like egoraptor did between castlevania games (and between megaman and X) (and this might open up discussion about particulars others see or what to mention)
To me, I don't feel a player connection to the events of Cross, and I don't think the [main] characters do either. Furthermore, the game doesn't have a leveling system, nor any means of really conveying an intentional growth in strength or progress, so it feels stagnant in more ways than one. The music is nice, but often times doesn't really connect to whats going on, so it doesn't leave any lingering connections. (Btw, i listen to the soundtrack often enough,as it is nice music, but I don't think its good video game music)
The simplest improvement I can think of for the game would be to rename it, and cut out some of the lingering ties between the two games. Keep the Cross universe and events that happen with that particular sphere, and add a bit more backstory to the game's past and set-up on the events that I get from just that game alone. Yea, that doesn't do much for people that already played it, but if the game is better self-contained, then it can focus more on the a "new experience" esp if its ever rereleased with like revamped graphics.
More complex improvements would be giving Serge an outlet for expressing himself in the story. I don't think he works as a silent protagonist and could use some dialogue to intact with everyone else; esp if he gets inner monologue or thought bubbles. I think some other story-based presentations would need to be tweaked, and to have a change in character growths, story contributions, and to have inter-party connections all make more sense.
Again related back to Sequalitis; Cross is like castlevania 2 in many regards; just like how many elements of Simon's quest were revamped into later games and made to work, so could Cross elements be made and refined to make better chrono games; but these are tools that need to be used deliberately and with skill, not just tossed together because it might be neat or stir a potential moment of awe.