I use an older Pi with Raspbmc (osmc) and I can stream 1080P movies just fine. The key is to 1.) Avoid streaming off a slow disk e.g. NAS, 2.) Ensure you have the necessary bandwidth to stream (no slow wifi), and 3.) Pass DTS audio to your receiver for decoding so your PI isn't doing double duty for audio/video.
It is also worth looking at NFS if you use a NAS. I have been able to stream movies over terrible Wifi by switching from Samba to NFS. This wasn't with a Pi though.
but it wasn't good for streaming videos over the network. The router was the problem.
so when we upgraded to rasp2, I tried this setup..
disk [usb]-> raspB+ <-[eth]-> router <-[wifi]-> rasp2
..and it's been working like that, flawless, for almost a year so far.
The raspB+ shares the media collection over upnp, so we can consume it from pretty much everywhere on the house, and the rasp2 consumes using upnp so when can control it remotely.
With a combination of these apps, you can do pretty much everything remotely from your phone..
