Similar, yes. I don't have either camera but I do have a D7500 and a Z6 so my comparison may not be apples to apples. I attach my Sigma C 150-600 to the Z6 using the FTZ adapter with no problems. I do get more reach with the D7500 and that's where that lens stays 90% of the time, but I'm not able to notice any difference other than that. If my D7500 fell in the lake, I wouldn't feel compelled to replace it. I am quite happy with mirrorless from here on out. The biggest difference is probably the EVF vs OVF. I wasn't sure if I would enjoy using the electronic view finder, but I do. Some prefer the optical view finder though and others hate the EVF altogether. Also, the crop Z cameras use the smaller batteries. I like that my D7500 and Z6 (and even my ancient D800) all use the same batteries,(EN-EL15). I would suggest renting one, or at least buy from somewhere you can return it if you don't like it.
I own a Z50 and a D7500. Either camera will do a great job for stationary birds. Birds in flight are more of a challenge with the Z50 in my experience. That is not to say that the Z50 can't handle BIFs - it can. It's just that my keeper rate seems higher with the D7500.