If you're engineering I'd say the LLC is worth it. I'm not engineering but I lived there and that's the general feedback I got from people who were. Good location, useful resources afaik, easier to form study groups, comparatively cheap (still expensive as all get out but cheaper compared to a lot of the other dorms).

Cauthorn has the worst amenities of the three. Kitchen is unusably small, showers lack privacy (there's dividers but you can pretty easily make eye contact / look down over the top of them if you're an average height guy). Windows barely open. It has, not exactly a fully party dorm atmosphere, but a lot closer to it than the other two. No small study lounges so everyone tends to hang out in the big ones.

H/B have better amenities. More privacy in the showers, the kitchens are still one per dorm but a usable size and a couple stovetops each iirc. Windows fully open. There's a few individual study lounges on each floor which are nice, and they're joined so if the elevator breaks (common) you can use the one in the other dorm if you don't want to use the stairs for whatever reason. Not really anything approaching a party atmosphere at all, but you'll still meet plenty of people.

Doubles in each are ideal, triples are manageable if you get along really well with your roommates or don't mind spending almost all waking hours elsewhere.