I feel like I typed this response. I'd also echo your Eno choice and probably add in Funkadelic/Parliament, Stooges and MC5.
Bowie. His body of work is so eclectic, I could always find something for my desert island mood swings.
I think the topic has maybe kinda strayed from the original question? With people talking about "desert island" bands I instantly think Frank Zappa, as that would give me a great deal of variety out of a single "band". But, if considering the context of the original question - which emphasizes "total catalog" - I don't know that I could say Zappa, as there are a lot of albums I don't care for. With that context in mind I would probably have to choose a band with a very small catalog consisting of nothing but hits...and I don't know who that'd be off the top of my head.
Haha - my comment wasn't directed at you Biff! I had noticed a few peeps mentioning the "desert island" idea. And it made me think that my answers would be wildly different!