The Desire Z is more of a mobile internet/social networking device than a phone. If that is what your mother wants in a phone, she will like it. My personal opinion is that my previous phone (Nokia N97) is a bit better as a phone. The sound quality as a phone is slightly better on the Nokia than the HTC. You can have her try out the sound quality on your Desire and see if she is OK with it. I suspect that the Desire Z would be very similar to your Desire. If your mother likes your Desire more than her phone, she would probably be happy with the Desire Z.
The main differences between the Desire and Desire Z is that the Desire Z has an SLCD screen instead of the AMOLED on the Desire. Also, the Desire Z has faster download speeds than the Desire if your carrier supports it. Then there's obviously the keyboard. Also, note that the Desire Z is amongst the heaviest of smartphones. It is 180g compared to 135g of the Desire. I'm not sure how big a factor this would be. I don't mind the weight, but I do feel it.