Sorry for the late reply.
144hz only tells me the refresh rate. 1080p 144hz, 1440p 144hz, 4K 120hz (144hz overclocked) etc.
The new AMD cards are decent enough, but just like Nvidia, nearly impossible to get. 6800 just barely makes your price point. RTX3070 is a little cheaper.
Very generalized:
Radeon 6800 ~= RTX 3070
Radeon 6800 XT ~= RTX 3080
Radeon 6900XT ~= RTX3090 (Not worth the price tag, either of them)
Depends on the job/game the card is doing which is truly faster. Nvidia has a lot of neat software quirks still that AMD hasn't quite matched. Ray Tracing, Tensor cores, so it can do some things better. AMD has more memory, so might last a little longer in that regard.