"I am interested in learning Z80 assembler,"

No arguments on your preference. But why do you want to do that?

As someone had pointed out, I thought the Z80 had seen better days. The SPECTRUM (toy!) PC was based on it. In any case there must be a reason as to why you want to learn the z80

+ Professor says so.
+ The lab. has only Z80 kit.
+ The course material is based on Z80.
+ No other chip is available in my country.
+ The name Z80 is sexy and I like it..
+ I hate multiplexed address and data bus.

If the above are your reasons, you HAVE to learn Z80 irrespective of whether it is more powerful than 8051 or not.

If those are not the reasons, then you would do well to start off with the 8051 which is one of the most popular ones when it comes to microcontrollers. And the ISP chips with on board flash and few others with JTAG interfaces and some more with on board IIC, CAN are real pleasure to learn and use. OK when it comes to variety you may get 8085, PIC, SICK and so on and so forth.

But my preference : 8051

( Certain rhyming words are unintentional and don't mean offence to that religion of MCUs ;-)

Enjoy.

Raghu