So if i am correct, RTX = Nvidia and RX = AMD
is there a reason one would take one over the other or is it just what brand you prefer?
There are a few factors.
nVidia has the technological edge, they do make the faster cards. AMD then beats them by being cheaper. ie. a R10k nVidia GPU is likely matched or slightly slower than a R10K AMD GPU.
nVidia have DLSS. AMD has FSR. DLSS is better, though FSR has caught up a bit.
nVidia and AMD both have Ray-Tracing. nVidia call theirs RTX. nVidia is better at Ray-Tracing, however they are more expensive and RT is still fairly niche, not that many games support it and of those, it is only sometimes amazing, other times fairly meh. It is also a massive hit to performance.
nVidia generally have better driver support and stability. Not always true but on the average I would say they're probably more stable. The latest generation is also fairly power efficient, more so than AMD cards.
So if you want max performance, it's nVidia. If you want performance at a budget, it's AMD. If you also want max graphics with Ray-Tracing, it's nVidia with RTX and DLSS.
It's basically a trade-off between price/performance and then the additional features like RTX and DLSS and AMD's equivalents.
At your budget, I would take the AMD card if buying brand new and locally. They've been quite stable, fast and a better deal overall in terms of raw performance for the price.