I"m a vet student at Liverpool so I can't speak for Cambridge but if you have any questions re the course/city etc I'm happy to try my best and help. But since your main concern about Liverpool is accommodation, I just thought I'd try shed some light on that.
Regarding flatmates going out more than you, if this is a huge worry and it's feasible financially, you could consider a studio? Other than that it is just luck of the draw with flatmates. But you might be surprised how much some vet students go out, even with the course load! It can feel very much like work hard, play hard. But however first year goes with halls, most people tend to leave halls and go into a student house with friends for year 2/3, and then for years 4/5 you leave Liverpool and most people find a house on the Wirral, so you can have much more control over who you live with after first year and find people on your wavelength.
If going out isn't your thing then there's so much to do in Liverpool that isn't just clubbing, and there's vet events throughout the year as well. You get your vet freshers week which ends with a party at the Leahurst campus, then there's also vet halloween, the winter formal, the Leahurst Christmas party, and the summer ball, as well as any others that your year reps might organise throughout the year.
Hopefully this helped with your worries about accommodation, lmk if you have any other questions.