Is the service on club level pretty much the same at any of the hotels at Disney that offer it?
Yes and no. We are lucky enough to have stayed at least 1 night at nearly every CL lounge. (FYI, we also like values and mods) In general, all CL's are similar. The only clear cut unique perk I can think of is the special safari offered at AKL for just AKL CL guests. I haven't tried it. Also, the semi-CL offered at CSR is slightly different (no APO).
The personality of each CL is unique, with small differences in food, unique to each theme. BC has Sam Adams beer (Boston), but so do most CL's. AKL has the special "Safari Amber" unique to AKL/AK. All have Bud Light.
One variation is part of the 5-7pm food- most food is same/similar, but each CL has a few 'unique' offerings, often dumplings, in the resort's theme. Poly has meat skewers ('Ohana), BC has tiny portions of lobster salad (1 day/week = NE), Med salads at BWK (Kouzzina)...Then again, most CL's offer a Tomato/mozzarella/basil salad and meat skewers once a week.
Breakfast- the most important offering - is basically the same: slightly different fruit, or slightly different pastries. IMO, muffins are muffins. All have latte machines- but two different types of machine: Nescafe or Nespresso. Push button lattes are a great perk! Also, say goodbye to nasty refillable mugs and paper plates. Yippee! Unless you want them! CL guests get real dishware! (or paper)
The layout of each CL is probably the biggest difference. There are also small differences in the personalities. BC has IMO the best service, but the lounge does not offer the view that CR/Poly offer. They have stunning views of MK, including Wishes. WL is 'rustic'- stew/cobbler. GF is slightly upscale. AKL has great view of AKL lobby. CL's are CL guest access only. The whole CL floor/building is CL guests only, so it's an added level of privacy/security. There's also a convenience factor that's hard to describe.
Always though, like any place else at WDW, so much depends on the personality of the staff you happen to get. Most are very good. CL means extra service. Hard to pinpoint what that means. Some folks don't use it, others love it. I see it almost like
trip insurance: run into an issue, and they can help solve it quickly. They can't do everything, or make miracles happen, but CL guests avoid most of the (in-resort) line waiting.