Just tried this game on my R9 Fury using the latest 16.4.1 drivers. The game works fine for a few minutes then it starts to stutter especially if I drive/fly through the city and after a few minutes randomly crashes - I checked with a monitoring software and the stutters are happening when the VRAM usage is nearly full.
CPU: i7 4790k
RAM: 16 GB
OS: W10 X64
The game runs from an SSD.
Lowering texture settings from High to Normal fixes the issue - no stutters, or crashes. When I change the settings the game shows the VRAM usage is "acceptable" so I think the (driver?) memory management for some reason has issues with higher res textures.