How to compare the efficiency of public key cryptosystems, i.e., RSA vs El Gamal?
Since you are approaching this from the point of view of mathematics, I think the most fruitful avenue would be to look at asymptotic performance and security of the problems that the cryptosystems are based on.

For example, with RSA you need a modular exponentiation for every message you encrypt or sign. The time that takes depends on the length of the modulus as well as the exponent. The most efficient general purpose algorithm for breaking RSA is GNFS which also takes time dependent on the size of the modulus.

Find out the same for the other algorithms you are interested in and you can compare them and see e.g. whether one will asymptotically become more efficient at equal security.

This will allow you to steer clear of the various practical issues of how the different constants compare and what platform some performance measures might be relevant for.