The z80 speed vs today’s modern processors

I have no idea how to make such comparison, even because there are so many metrics (i.e.: integer performance, branching, floating point operations, cryptography, execution of a given script language, etc) and many of those wouldn't even apply for a z80...

The easiest way to make people understand how difficult things are for a z80 nowadays is to tell that most webpages simple logo images won't fit the address space of 64KB that it can directly address, that it has no provision for simple tasks (nowadays) like multiplication, division, floating point operations... Just telling it is 10000 (or whatever number of times) times slower won't even scratch the surface of how impossible it is to even make a mundane task like render a google search webpage because SSL would take 3 minutes to make initial handshake and then you have all those scripted content...

People has no idea of how much resources are used to render "mundane" tasks nowadays, they just take it for granted, probably they will say: ok, it is that slow, but still like an old phone it will take 20seconds to open a google page but it will do it... :P

I remember that 10 years ago my notebook had about 300.000 times the power of my Z80 machine.
I had to explain this to some people at this time:
When you build a line of 300.000 Z80 machines (in my case an Amstrad CPC, but for an MSX it will be similiar) it will have a length of 160km, which is about the distance from Amsterdam to Roermond.

Salutte created a benchmark suite for different languages (assembler, C, Fortran, etc.) for MSX: https://github.com/MartinezTorres/z80_babel

Since some are in high-level languages with compilers for both z80 and modern CPUs, that seems to me like a very simple way to get an approximation. Of course, getting to run one of the classic standard benchmarks like Dhrystone, but the advantage is that is should be pretty low effort to get numbers (as Salutte already calculated the numbers for MSX).

I think it all depends on what you want to test. There are several aspects that you can test in terms of speed. How fast is each instruction, but also if things are missing in the CPU compared to another CPU, this must be done on a slower work around.
A modern CPU has several layers of cache that can help a lot in performance. CPUs also have hardware multipliers and dividers for integers as well as for floating point calculations. And lots more. The Z80 does not have all this. So a fair comparison should include this.

If you just wanted to compare the CPU, a prime numbers calculation would probably be a good one. It uses a lot of these functions including multiple cores. But with this you don't include the video interaction or moving large blocks of memory internally. But I think that you're not looking for an exact here, so this should suffice.

Mine is just an observation that the emulation despite faster processors and still behind. It is no coincidence that we talk about FPGAs as the future for this sector