ShinyChrome:
I am a big fan of LG's webOS, as you will see a few posts up me heaping praise on it. It is the one redeeming feature of my current TV, and probably about the only OS I would bother using built-in apps. Too bad that LG's LED TV range is all IPS and the OLED range is more than I want to pay for a TV right now.
The Xbox on the other hand, I find the streaming apps to be slow, clunky, and buggy. I'm pretty fussy about UX and spoiled by webOS though, so maybe its just me.
I must admit, getting a Harmony remote has improved my experience with it somewhat, but I still feel gaming is the only first class experience it offers. The other functions can be done better by individual devices (UHD blu-ray player, Shield etc), but obviously at added cost. But if you can only afford one device and it does everything you need, then by far it is the most cost effective option.
Yeah webos is pretty great. Can be a bit slow at times, but it's pretty solid. Range of apps is pretty good too, TVNZ on demand and others I forget - other than the spark sport cluster (i have a 2016 model).
Xbox one apps - yes it seems not as much care has been put into them perhaps. Overall though I'd say they are decent enough netflix, plex, amazon - Other than youtube which is rubbish.
I will say I haven't noticed them being slower that the tv native ones - in fact anecdotally I'd say the xbox ones are faster.