You could easily start with game 3 in this trilogy simply because you do fuck all in the first two anyways.
Actually XIII-2 is fairly similar to CT at it's blueprint level. Jump the timeline, get a new macguffin/character related to the big bad, learn a tiny bit about the big bad, jump to a new timeline. Rinse and repeat until end game.
CT just does it better because there are actual 'time line changing events' besides a change in background coloration.
Also it doesn't end in 12,000 BC with Lavos showing up, frying Crono with his Jesus Beam, and posting "To Be Continued....". Plus the only thing keeping you from beating the game before the designated end is Lavos posting :frogout: with his "Destruction rains from the heavens..." attack among its other nasty attacks instead of "I have the Reraise! I have Reraised now!" schtick fueled by his invincible godmode powers and a literal Deus Ex Machina (which was the exact same problem the villain of FFXIII-1 had as well).
Also, Chrono Trigger barely ever took itself seriously and only really when dealing with Lavos and 12,000 BC (even 2300 AD had Johnny and the Sewers dungeon) whereas FFXIII-1 took itself so seriously it hurt and FFXIII-2 tried way too hard to not take itself seriously at all which, more often than not, led to most of the humorous scenes being more obnoxious than funny (and of course XIII-2 still had its painfully serious moments).
Plus the reason for why you don't just settle down at 1000AD after your initial adventure of rescuing Nadia and escaping from a bum trial and an impending execution is because you want to stop Lavos and you're the only ones who even know about it let alone do anything about it. Meanwhile your reason for going after Caius after your initial adventure of stopping a giant flan from chewing away at the Crystal Pillar so that nature and the elements can weather and erode the Crystal Pillar anyways was because Noel has a beef with him for some reason and because you think he's been fucking with the timeline but he really isn't because he's also immortal and is just goading you on into fucking with the timeline for him (all the while having a timeline fucking bomb strapped to his heart so even if you do stop him he'll just kill himself on your sword and detonate the timeline fucking bomb like a motherfucking jihadist). Also there might have been something about looking for somebody's sibling or something but damned if anybody can remember.
The resemblances are indeed rather superficial at most.