Help me

I have the OG Xbox one (3yrs old 1000s hours on) At my house that I play everyday and love and enjoy When I go to my cottage where I have a Xbox one S (maybe 30hours played on it) and when I play on it I notice a BIG gaming difference it’s slow, my movements are weird and I feel like a bot when I play. I have a 4K tv and contacted support multiple times but they can’t seem to understand