Should I Switch to HDZero with My DJI Goggles 3?

HDZero costs the same for the free style with a camera.
If you have it, saving money would not be the reason to change.
The only relevant reasons for switching at this point would be if you're worried about DJI products being taken away by regulations, if want lower latency, or if you just dislike DJI as a company. 

Edit: One other good reason for switching would be for flying in large groups where the bandwidth greediness of DJI is restrictive

Analog on time

I haven't used hdzero, so grain of salt.  I am not interested in the hdzero vtx's so much. Better range and penetration from dji, and also better picture.  The latency is the biggest deal, so if you are going to race it would be really important. Or maybe you would try it and wonder what you've been doing. But really for me it's one of the best if not the best analog goggle, and dvr. I think Orqa might surpass, but I haven't really looked. Hdzero is versatile. Analog/Walksnail/HDZero all available, and before you know it someone will make something, or they already have something for OpenIPC FPV. 

I'm all for HDZ, simply for the latency issue.  I'm not a racer, but when I switch over and use some of my WS stuff (I use a bunch of that for some work purposes) it just looks really "weird" to me.  I second, though, that the picture quality and penetration is way better on the WS gear though.  But flying freestyle on WS is just a very uneasy feeling for me vs. HDZ.  WS is good on more of my cine-type gear.  Good luck.