In my use of EVF, Sony NEX-7, Sony A99, Fuji X-E2, and E1, the only place they may let you down is in panning as some are slower than others to catch up with movement, and low light manual focus. The Sony Nex-7 was at times hard to focus with the EVF in low light, but for me the LCD with peaking was still excellent. Fuji's X-E1's EVF was a bit slow with either movement or low light, but the X-E2 seems to have improved on this. In low light the EVF will always have more issues with noise in my experience.
I feel that Fuji's big mistake on the X-E1 and X-E2 was to not figure in a way to have an eye cup around the EVF finder window. Sunlight coming in over your shoulder can make using the Fuji EVF tricky at times. Sony has always had a good solution here. I noticed that on the pre-shots of the X-T1 Fuji seems to have placed an eye cup around the EVF finder window.
The trade off is the fact that you can zoom in with peaking which I have gotten very fond of. Nikon and Canon can come close with Live View on their LCD"s but many times in the outdoors, the ambient light makes focus from the LCD hard to do.
My for work, I still miss the tiltable LCD, and if Fuji puts that on the X-T1 that will be a big plus.