I assume you mean Gamecenter? Center Ice is the TV package, Gamecenter is the streaming service.
MLB Advanced Media runs Game Center, so I would assume it's mostly the same as mlb.tv. I've gotten Gamecenter in the past and really liked it. Every game in HD, you can choose which broadcast, archives, etc. All the usual bells and whistles.
If you are asking about Center Ice, which is done through your cable provider, then I would say it is more comparable to Extra Innings. I love it.
Comparing it to MLB.tv, which I tried this year, well.... let's just say I am going back to Extra Innings next year.
Edit: The reason I say this is that I have found the internet is more prone to lag and stuttering than EI through my satellite. I could deal with it for baseball, but I wouldn't be able to watch hockey like that. With that said, I have no idea if it was my ISP, hardware (which, it shouldn't be as my modem and router are both really, really good), or the MLB.tv app itself, so you may have different results.
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