The EVF on some of the newer bodies is breathtakingly good. You can set it up to either make the image brighter or to reflect exposure settings (i.e. reflect what the recorded image will look like based on your current camera settings). You can also zoom in to ~100% (depending on camera model) which can be quite useful for manual focus. Not something you can do with an OVF.
Historically there could be issues with lag, shutter blackout, etc. with EVFs. But these issues have been overcome with newer and more advanced tech. Focus also tends to be better with an EVF compared to a DSLR using the OVF since focus is acquired from the sensor data—so you don’t have to calibrate lenses to your body (which can be a very frustrating process since lens calibration only works for specific apertures and subject distances (and focal lengths in the case of a zoom)). An EVF takes many of these focus issues off the table since what you see through the EVF is what you get.
The EVF on the Sony A1, Leica SL2, Nikon Z6/7 is fantastic, speaking from personal experience. Better than an OVF. The EVF on the A1 and SL2 in particular are quite literally breathtaking. I can’t speak to other brands/bodies as I don’t own them, but I imagine the EVF on newer bodies from other brands to be similarly good. Over time, I expect most/all EVFs on any camera body to get to this level.
Currently it is hard to shoot with my D850 after experience shooting a body with a good EVF. The OVF is just inferior from a practical standpoint and its LV is also lacking compared to my mirrorless bodies. For me, my mirrorless bodies are just better in every way. For me, there are no downsides to mirrorless vs a DSLR from a shooting perspective.
The only potential “gotcha” for me with mirrorless has been the possibility for PDAF artifacts in the final image with some mirrorless bodies (i.e. artifact lines in the final image from the rows of “dead” pixels devoted to AF on a PDAF mirrorless sensor). Was sometimes a problem with my Sony A7R3 or Nikon Z7 depending on how I processed the image in post—annoying lines that can be challenging to remove. Not a problem with my Leica SL2 (as it doesn’t rely on PDAF for focus—there aren’t any linear optical “holes” in the sensor). Hasn’t been a problem with my A1 (though not quite sure why not as it relies on PDAF technology—but it hasn’t, even when really abusing the files in post).