Basically screwed either way. You can actually get high end Nvidia GPUs and monitors. Getting a high end free-sync monitor, pretty easy. Getting a high end AMD card, not so much. Either way you are locking yourself down to either vendor (unless you don't mind selling monitors and GPUs regularly)
Free-sync monitors tend to only work at fairly high refresh rates, so the minimum free-sync range is something to look for. Not much use if Free-sync doesn't work when your GPU can't keep up. Free sync can work over HDMI and DisplayPort. Since the normal scalar is used, the monitor may also offer DVI and VGA ports if that matters to you.
G-sync monitors usually have a good range, down to around 30 FPS. So they'll keep it smooth even if you are asking way too much of your GPU. Limited to display port only. G-sync 2.0 monitors also have an HDMI port, but G-sync doesn't work on them.
Direct comparisons usually leave people unable to tell which is running. From the TFT Central reviews, they usually give the edge to G-sync in terms of latency (input lag). But that makes sense, it is Nvidia all the way between the GPU and the panel. Everything else is basically up to the panel, so color, viewing angle, response time. You'll see the same panels from both vendors.
I guess it really depends on what GPU you are after. If you are going for say a 1080p 120hz panel and a GTX1060/RX580, you can probably forgo syncing techs. If you are going high end with a 3440x1440@100hz or 2560x1440@144hz then you'll probably want it. Though you would need to be looking at Vega or GTX1070 and up for those panels.