I have the same problem and tried it with a clean boot, to no success.
My DxDiag is attached.
I have an i5-4690K, 16 GB Ram, GTX 970, Windows 10 64 bit, two screens and installed it on an SSD. Nothing is overclocked.
It runs smoothly on Ultra settings in singleplayer (well, "smoothly" when you disregard occasional loading-stuttering, especially in videos). It also runs smoothly on empty servers.
When joining a session, the framerate drops not immediately but over a few seconds.
Game and Origin are running as administrator.
According to the Task manager, BFV has a network load of ~200 kBit/s, which seems very low to me. I have a 50MBit/s connection, and opened the TCP-Ports 80, 443, 5222, 8080, 9988, 17502, 20000-20100, 22990, 42127 and UDP 443, 3659, 14000-14016, 22990-23006, 25200-25300, and also activated UPnP and cleared my NAT cache. I don't run any network-limiters or so.