It sounds like you have a similar intrigue that I do into insanely tiny time.
When I first built computers in the 70s, 450ns was the typically static RAM access time, and at the time we were amazed at that.
Although I do plenty in RF mostly in S band and below (although I have been known to go up to K band experimentally), pretty much everything is measured in the frequency domain.
Much more recently, I have become more interested in looking at stuff like transmission lines in the time domain as well (as well as the frequency domain with VNAs as I traditionally have done), and it gives an interesting, and different, perspective.
What I would say is that if you did go to a 1GHz bandwidth scope from a 500MHz one and are trying to measure ~300ps rise times such as with the JW pulse generator, there is a difference, but it's nowhere near as much as you'll get with a sampling scope in the 10s of GHz. What I would recommend, if you go for a real time scope in the low GHz is to get one that works in equivalent time too. Neither interpolation nor fixed, limited period sampling give a faithful reproduction of what's happening, there will inevitably be some bastardisation, but with ETS you can avoid the interpolation and sampling period limitations, and will generally get a fair bit closer on repetitive signals.
Even with ETS, typically the next problem to deal with is front end analogue artefacts like overshoot and/or ringing that often might only exist inside the scope! One way to show what's happening is to shoot a step from a TDR such as that in a sampling scope set up and look at the response when it hits a 1GHz scope's BNC, it's rarely pretty.
A high speed sampling scope is not the same as a regular day to day scope, almost like a spectrum analyser isn't like a regular scope or a kettle isn't an oven, they are different tools for different jobs. My guess is that if, like me, you invest in a 1GHz scope after using 500MHz units, it's just won't be enough.... you have been warned!