It is at this point in my blogging career that I get the nagging feeling that I should have read my White Wolf books in something approaching a chronological order. Trinity has a refined and updated version of the basic Storyteller system, but I'll be damned if I can put it into any kind of historical context. I can tell you how it's different than, say, Vampire, Revised or Exalted 1st edition, but in terms of progress, fashions, or other general trends? I got nothing.
Overall, I'd say it's an improvement over the World of Darkness version of the system. It's certainly no worse. Fixed target numbers make probabilities easier to eyeball, though the new way of figuring difficulty doesn't have much resolution at lower levels Basically, given the dice pools involved, there is a significant difference between requiring 3 successes and requiring 4, but not much between requiring 1 success and requiring 2. (The probabilities, with a relatively modest dice pool of 6 are approx - 95%, 77%, 46%, and 18%, respectively - I could probably have proven my point more dramatically with a size 8 dice pool, but that would have been a pain to calculate). It's not something I'd say rises to the level of a problem per se, but it seems likely that someone who was both a fan of the Storyteller system and naive about probabilities might think that Difficulties 1-2 are more of a barrier than they are likely to be in practice (if only because players are, with few exceptions, unabashed character optimizers).
There are other streamlining features. Soak is no longer rolled. Demeanor is a thing of the past. The system generally moves faster. It's just a shame they left in the two biggest Storyteller system time-wasters - multiple actions and extended rolls. Those continue to grind the game to a halt whenever they appear, and the combat system, for all its improvements, still basically requires players to at least try to split their dicepool between attack and defense. So there's a way to go.
Changes aside, Trinity definitely feels like a classic White Wolf game. It has the same basic tropes - characters who start as "normal" and then get generally better by becoming a supernatural entity. It winds up being a little offputting here. Psions get psionic powers, which, of course, totally fair, but then they also get two extra attribute points and the exclusive ability to use the best biotech? For a game that is ostensibly pushing the "psions are just humans with psychic abilities, unlike those Aberrants who allowed their superpowers to corrupt them" story, it seems an awful lot like psions are supposed to be considered a superior form of life.
Although, with the typically broken Storyteller-system character creation being the way it is, the loss of points is not necessarily as big a disadvantage for neutrals as it could be. Trinity also has the distinction of basing the psions' power stat off of a formula derived from their attribute ratings, so there is an extra point where character creation can result in wildly divergent character point totals.
The other big White-Wolf-ism I noticed was psychic attack powers being noticeably less effective than shooting someone with a gun. Granted, the guns here are futuristic sci-fi lasers, but the principle is the same - as much of an advantage as a perfectly concealable weapon is in real life, the circumstances where it's an advantage in the game are much rarer. "Oh, an Orgotek Hornet VI Pulse Laser can only be concealed in an overcoat? I guess I'm just wearing an overcoat wherever I go, then."
But I know the real technological question you've been dying to know the answer to - "what dumbass thing did have in their sci-fi future that fills the same niche as a smartphone while somehow being infinitely worse?" And I have to say, to their credit, they almost got it. A mini-comp has roughly the same dimensions as a smart-phone. I know because I measured mine with a ruler and compared it to the measurements provided. The only one they got wrong was thickness, which they listed as 3cm instead of 1cm. Its user-interface is unwieldy (foldable keyboards) and it has too many peripheral slots. Also, there's no mention of battery life, which is the sort of detail that of course would needlessly bog down an rpg, but would be the first question I'd ask when buying one. But really, they came pretty close.
My personal biggest takeaway from the equipment section was that people of the 22nd century are going to perform overwrought sadness when their blankets die, but knowing human nature, these performances are going to be a maximum of 49% ironic.
(Oh yeah, there's a blanket. It's alive. When it senses that you're cold, it can crawl over to you and wrap itself around you. If you're in extreme danger, it can act as medical life support for up to three days before it "exhausts its own resources to maintain the user's life." - Not mentioned in the book: the 2-week delay between when they're first released onto the open market and when the first one gets an anime waifu printed on it).
UKSS Contribution - I'm going to go with ISRA, the Clairsentient order. They have psychic powers of prophecy, they're hippies, and they live on the moon. I probably won't cleave too closely to their overall backstory, but I can definitely find a use for psychic moon hippies.