The MI8 card's HBM has a great power and performance advantage (512 GB/s peak bandwidth) even if it's on 28 nm. NVIDIA has nothing that has even remotely comparable bandwidth in this price/perf/TDP regime. None of the NVIDIA GP10[24] Teslas have GDDR5X -- not to surprising given that it was rushed to marked, riddled with issues, and barely faster than GDDR5. Hence, the P4 has only 192 Gb/s peak BW; while the P40 does have 346 GB/s peak, it is far higher TDP, different form factor and not intended for cramming in into custom servers.
[I don't work in the field, but] To the best of my knowledge inference is often memory bound (AFAIK GEMV-intensive so low flops/byte), so the Fiji card should be pretty good at inference. In such use-cases GP102 can't compete in bandwidth. So the MI8 with 1.5 the Flop rate, 2.5x bandwidth and likely ~2x higher TDP (possibly configurable like the P4) offers an interesting architectural balance which might very well be quite appealing for certain memory-bound use-cases -- unless of course the same cases are also need large memory.
Update: should have looked closer at the benchmarks in the announcement; in particular the MIOpen benchmarks [1] MI8 clearly beating even TitanX-Pascal which has higher BW than the P40 indicates that this card will be pretty good for latency-sensitive inference as long as stuff fits in 4 GB.
[1] http://images.anandtech.com/doci/10905/AMD%20Radeon%20Instin...