New Graphics card?

I guess I'm probably asking this of the BBS gamers, and I'm going to apologise in advance if the answer is as obvious as I suspect it may be... :)

I have a PC permanently hooked up to my TV. The guts of it are:

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16GB Ram
AMD Radeon R7 200

When I'm watching streamed (HD) football through the PC I get just the tiniest 'judder' in the display which I don't get when watching it via BT Sport - which is also streamed.

Now I absolutely accept that given BT are chucking 40Mbps at me then their picture ought bloody well to be buttery smooth. Having said that, I subscribed to PremierLeaguePass last season which also provided an excellent HD stream... but viewed through the PC with this slight judder...

I am going to rebuild my main PC, which will free up the internals to rebuild the 'Media Centre' on a hand-me-down basis. My main PC also runs an AMD Radeon R7 200 but has this spec:

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16GB Ram

So, what do you guys think? How much of the issue is likely to lie with the R7 200; will the overall spec improvements help or should I just shut the **** up and see what happens when I rebuild with what I have? :)