Looked into this a bit more. The GTX 1080 is based on the Pascal architecture and so will be faster than any Kepler-based K80 on any cloud - even faster than a K80 card with 2 GPUs. The GTX is a consumer board and is less expensive than the datacenter equivalent P100 PCIe card. The P100 has 16 GB ram and HBM2 memory (twice the memory and more than twice the memory bandwidth) and supports ECC if you care about detecting memory corruption. The P100 will be faster than the GTX 1080 once it is available. As I said before,
GCP offers K80 GPUs in passthrough mode and you can use a single K80 die ($0.70 / hour billed by the minute) or you can attach up to 8 K80 GPUs to a single VM. Disclaimer: I am a product manager for GPUs in Google Cloud.
The P100 is about 10x the price of the 1080 ($6000-9000 vs $500 for the 1080 and $700 for the 1080TI).
I've talked with several second-tier cloud providers, and the GTX 1080TI is what their large-deployment customers use. At the NVIDIA conference they were all promoting the P100 (NVIDIA insisted), but all admitted that nobody asked them to deploy P100s at scale.
The Hetzner box is about 0.15 an hour. That means more GPUs per developer.