a 1080ti will just sit idle most of the time. the image quality will depend on the content itself and mostly on the monitor and configuration (resolution, color ...).
see, when looking at that sort of content there is very little processing going on. maybe on high quality video you could see a difference but i doubt it.
when it comes to slow or sluggish browsing the culprit tends to be slow network, shortage of ram, lots of disk activity due to that, a slow cpu, and the fact that nowadays web content is often overloaded, not very resource aware and often straight out reckless. as computers become more capable, web developers become more daring and lazy. this will burden all mentioned components much more than the graphics card, plus there is of course the ubiquitous spyware which is not free: e.g. each time you open any half popular web page your browser is making dozens of requests to other ad sites taking a hit on your bandwidth and response time. each of these requests also involves some code snippet that uses the browser's ram to do its thing, by which it's also making the cpu work. ideally you should install an ad blocker but bear in mind that constantly filtering out all these request is process too. since this can happen up to 50 times on each single page view, after opening several tabs some or all those components start to hit their limits, specially ram, and you start to get 'slow browsing' syndrome. it will hardly be because of the gpu not keeping up with images, any integrated gpu should be able to do that just fine, with the same quality, unless you are specifically doing image processing, even then the difference will be only speed.
