Sony have more experience when it comes to remote play, but PC and XO is both made by MS. So, which feature will work better (do you think), when it comes to stability, resolution, framerate, latency and etc.?

Same network? Equal.

Over the Internet? Sony.

Agreed

Windows10-PCs: XBO
Other Windows-PCs: PS4

But since when has Sony more remote play experience than Microsoft?

Sony's Remote Play: since 2006
Microsoft's Remote Desktop Protocol: since 1998

Pointless putting polls in threads like this as PS4 fans just vote for PS4 and Xbox fans just vote for Xbox, Until we see how the PS4 - PC wins there is no way to know what so ever.

I can't really see there being much of a difference. I have a PS4, but I see no reason to ever use this feature, since my PS4 and PC are right next to each other and connected to the same TV.

Pretty much as far as things are on here. Though I honestly don't see the point in streaming a game from a console to another screen.

To elaborate on my previous post:

There's not much more you can do to increase stability through same-network streaming aside from plugging in with a cable. They'll just have to live with being equal.

As far as over the internet is concerned, Sony has an actual case to present, whereas Microsoft is restricted to same-network only.

Before you start questioning the PlayStation's online Remote Play, I can attest to its reliability: I bring my daughter to my mother's once a week so they can spend time together (my mother may not be here to see her grow up, so I want them to spend as much time together as possible). This is an hour away, and packing up my PS4 to take with me everytime is a major hassle. Instead, I Remote Play on my Vita, and wow, it works. But only on the Vita, for some reason. PSTV and Android don't seem to run as well, but on Vita I'm capable of running group chat in the background and play multiplayer on Dark Souls 2 with about a quarter second latency. And THAT is impressive to me.

Im really looking forward to seeing how it works over wifi on my laptop so if im ever in my friends house we dont have to play split screen, games like diablo 3 are far better on separate systems

Xbox One to Win 10...since it fully supports X360/XBO controllers.

Not to mention Remote Play on Ps3 to Vita was trash, and my Shield Portable to PS4 Remote Play offered a better experience for me thru a 3rd party app than the Vita/PS TV did natively.

In any event, none of it matters. The Lag is the deal breaker.