How to compare processor speeds based on architexture
This can be done if the target application is defined.
The easy way is to Write the code to solve a specific problem in a high-level compiled language and use a compiler that uses the full instruction set of the target. Then run the solution and benchmark it.
This can be done even between for example 4 bit CPUs with no cache and high end pipelined 64bit CPUs.
Don't forget that most modern so called CPUs are actually systems on chip SoC that include multiple cores, dedicated peripherals and coprocessor alike as the GPU and those can be used to boost the application speed. Also one of the most important things is code optimisation, you can use assembly for some applications but it is rarely used these days because it significantly increases the development cost so, the compiler is critical you can actually have a faster CPU running your application slower because of this.