If underflow is the issue, you could simply compare the sum of their logs (the mean of the logs is entirely equivalent)

Note that Fishers method actually compares $-2\sum_{i=1}^k \log(p_i)$ to a $\chi^2_{2k}$ ... so Fisher would also work on the log scale.

However, it's not clear to me that there's necessarily any particularly meaningful comparison between two sets of extremely small p-values. For starters, the values in the extreme tail will tend to be quite sensitive to even small deviations from assumptions.

Some people would argue that you shouldn't compare p-values at all.

If underflow is the issue, you could simply compare the sum of their logs (the mean of the logs is entirely equivalent)

Note that Fishers method actually compares $-2\sum_{i=1}^k \log(p_i)$ to a $\chi^2_{2k}$ ... so Fisher would also be working on the log scale.

However, it's not clear to me that there's necessarily any particularly meaningful comparison between two sets of extremely small p-values. For starters, the values in the extreme tail will tend to be quite sensitive to even small deviations from assumptions.

Some people would argue that you shouldn't compare p-values at all.