Best choice of finite field for AES on a 4-bit microcontroller? As the finite field of $GF(2^8)$ are isomorphic to $GF((2^4)^2)$, $GF((2^2)^4)$ and $GF(((2^2)^2)^2)$,
which of the fields is best suited and most efficient for 4-bit MCU and why? Would it be $GF((2^4)^2)$?
While $GF(2^8)$ is indeed isomorphic to $GF((2^4)^2)$ (and to the other fields you have mentioned), if you use the latter you will need a conversion routine to change the field representation from and to $GF(2^8)$. This will probably defeat any performance gain with the alternative representation (and I'm not sure there would be any). Another related issue is that the "nice" constants used in MixColumns (2 and 3) may not be so nice in the converted form, hurting performance when you multiply by them.

You can simply represent a $GF(2^8)$ element using two 4-bit words.