Should I sell the NIKKOR Z DX 50-250mm f/4.5-6.3 VR and buy a AF-P DX NIKKOR 70-300mm f/4.5-6.3G ED VR and a FTZ II mount for the same price?

I bought a Nikon Z50II that comes with a 16-50mm lens and a Z DX 50-250mm f/4.5-6.3 VR lens as well. I want to photograph some birds in the woods, I have the opportunity to sell the Z 50-250mm and with that exact same money buy a brand new AF-P DX NIKKOR 70-300mm f/4.5-6.3G ED VR and a FTZ II mount, do you guys think it's a good trade? The extra 50mm for birding (that in a ASP-C sensor is 75mm more) are making me want to do the trade but is it really worth it? And is the Z 50-250 better quality than the AF-P 70-300?

I know that 300mm is not exactly the best for birding but I don't have any more money to waste, so this is the only lens I can really get because like I said it's like a trade, it's the same money, I can't get anything beyond this.

Thanks