We usually tell people to use both since nostr.wine has regional mirrors and is faster, but notes do propagate to both so you can do that if you want. 

There are benefits but they require performant clients (that don’t just connect to whatever relays they want) otherwise you won’t notice. If I run Damus or Amethyst and use only nostr.wine/filter.nostr.wine the speed is genuinely unreal compared to pulling the same notes from 10+ public relays. 

Try this for a week and see how quick it is. After that check your battery use + data consumption. And all that is before you even use the built in (optional) WoT to browse global of 10+ large free relays (not all clients provide WoT out of the box).