Anyway (yes I'll get to the point eventually ^^ ), what I wanted to know is : how in your opinion is Triss a "better" person when she is with Geralt? What does that relationship bring her?
The first thing Triss gets in the books is the discovery that relationships can be deeper than the shallow ones she has known among the mages and nobility. This is somewhat tragic for her in the books because Geralt is bound to Yen.
When Geralt and Triss argue, it's about big important questions that force them to think. At Kaer Morhen in the books they argue about participation in wars, and whether great causes are worth dying for. There is a bit of a reprise of this discussion in the tent in the Witcher 2 prologue when they discuss Foltest's war agains the La Valettes. Their challenging but respectful arguments seem like a very healthy thing for both of them, and she probably enjoys being around someone who will dive into big philosophical discussions.
In Witcher 1 I think Triss and Geralt have a very good working relationship- they joke around and tease each other while working toward their goals. Geralt helps her to enjoy the work she is doing, and he has a good sense of humor. We get to see some more of this in Witcher 2 and 3 when Geralt's sense of humor lifts her out of a serious mood.
Another thing Triss gets from Geralt is someone she can trust and rely on. They do a lot of watching each other's backs in both the books and games. Geralt takes care of Triss when she falls ill in Blood of Elves, she watches out for him on Thanedd and saves his life there. They have a long developed comrades-in-arms sort of bond that means a great deal to her. With Geralt around Triss doesn't hesitate to take on dangerous tasks like wading into Vizima's sewers to face a zeugl, attacking a base full of Salamandra mutants, or trekking through Flotsam's monster-infested swamp.