For much closer performance you should get a 2080ti, which should be roughly comparable in speed and have 11GB [edit: wrongly wrote 14GB before] of memory (against the 16GB for the V100). Price-wise you still save a lot of money, after quickly googling around, roughly $1200 vs. $15k-$20k.
But you still lose something, e.g. if you use half precision on V100 you get virtually double speed, if you do on a 1080 / 2080 you get... nothing because it's not supported.
(and more importantly for companies, you can actually use only V100-style stuff on servers [edit: as you mentioned already, although I'm not 100% sure it's just drivers that are the issue?])
[1] I've not used 1080 myself, but I've used 1080ti and V100 extensively, and the latter is about 30% faster. Hence my estimate for comparison with 1080