I'm looking to build a PC for deep learning will tensoflow work on amd GPU with the same speed as on nvidia ones as amd doesn't have tensorcore or cuda cores but it will have 16gb of hbm vram his much do the tensor cores impact training
Tensorflow only works with Nvidia gpus. There are solutions that allegedly also work with AMD, but it is certainly easier to set up the original cuda variant.
It is difficult to make a broad statement about which hardware acceleration product has the best performance for deep learning until some comparative metrics using the same algorithms and data sets are published, which requires the availability of both products. It's anyone's guess from the below spec comparison. The information on the net is and could only be conjecture at this point.
AMD Radeon VII Vega 20 GPU 16 GB HBM2 memory 1 Tb/s memory bandwidth 60 compute units 3,840 GCN 1.8GHz stream processor cores expected price $700 (possibly lower due to 7 nm lithography) software ecosystem set up difficulty: high NVidia RTX 2080 Ti GeForce RTX 2080 Ti GPU 11 GB 352-Bit GDDR6 14 GHz eff memory clock 4,352 CUDA 1.5GHz stream processor cores PCIe 3.0 current low side of newegg price $1,189 software ecosystem set up difficulty: medium