The 1080ti has absolutely no competition from AMD in terms of performance/power and availability for most workloads; calling it "old fashioned" is... out of touch. And Nvidia is already on the move with Volta, which AMD will seemingly have zero answer for. They're running circles around themselves at this point.

If anything, Ryzen's increased PCIe lanes are a reason to go for nvidia. You can get Threadripper and mobo at a much smaller cost than a Xeon rig, with more lanes, but just load it with Pascal GPUs. And they'll have better performance, power, and be easier to buy than any Vega card. This would do quite well for a deep learning machine, for example.

The place Vega has advantages are in more niche areas, like open source Radeon drivers, fully unlocked FP16 support (garbage market segmentation from Nvidia), and the Instinct/SSG GPU lines they'll be offering will be unique. And they're definitely cheaper, for sure. (But unless AMD can back it up with software, it won't mean much, especially for markets like deep learning, which NVidia is going full-force.)

How are VEGA different from the 1080 in this regard ? they're designed with more parallelism in mind ?

Vulkan was based on an API design by AMD but that doesn't mean it works better with AMD hardware. From Mantle to Vulkan there has been many small changes to make it perform optimally in pretty much all modern GPU architectures.