Given two infinite sets $X$ and $I$, and a filter ${\cal F}$ on $I$, one defines as usual the equivalence relation $\approx_{\cal F}$ on $X^I$ and obtains the reduced power $Y = X^I / \approx_{\cal F}$.

Question 1 : to what extent do such reduced powers differ when one filter on $I$ is changed to another filter on $I$ ?

Question 2 : consider question 1 in the case of different ultrafilters on $I$, thus in the case of ultrapowers.

Let me specify my question. Given two ultrapowers $X^I/F$ and $Y^J/G$ where $X,I,Y,J$ are arbitrary infinite sets, while $F,G$ are ultrafilters on $I$ and $J$< respectively, the questions is to what extent :

1) the cardinals of those two ultrapowers can differ ?

2) those two ultrapowers are not isomorphic when $X$ and $Y$ are fields ?

A more precise, and at the same time, more general form of the question is as follows : Given a reduced power X^I / F, where X and I are arbitrary infinite sets, while F is an arbitrary filter on I, to what extent does the reduced power X^I / F change, when X, I or F are changed ?