It's much better today than it used to be...absolutely. There's a lot to cover when cross browser testing, but this should give a good overview: https://developer.mozilla.org/en-US/docs/Learn/Tools_and_testing/Cross_browser_testing/Introduction

The main thing here is knocking out the unknown unknowns...when you have browsers sharing the same underlying rendering tech you can anticipate and deal with the same quirks that come up with those..instead of having to redefine solutions. Aside from rendering, there's still going to be technology each company builds on top of that base which will still be proprietary, but at least when you're looking at different form factors and different platforms, there will be a lot more in common with the most popular browser, Chrome, than not..which helps. That's all.