I think there's a pretty good profile of the firm available here:
https://directory.thecorporatelawacademy.com/profile/travers-smith.19
I think they're essentially kind of a SC version of Slaughters, but with particular expertise in mid-market PE (funds, finance, M&A between £100-500m), and I think their "room-sharing" system is a USP especially for training (up to six people with seniority anywhere from partner to trainee sitting together so you get a range of experience and opinions to learn from). Also everyone I've met from the firm raves about Braithwaites (inhouse canteen) but I don't know if it's actually appropriate to mention that in the cover letter
@Afraz Akhtar can probably provide more detailed insights as he's a future trainee at the firm!