How do I find the odds in a dice pool contest?

Im designing a system where overall success is determined using a dice pool where you count the number of max-value faces among dice rolled and compare this number to some difficulty number. In this system you roll d6s for attributes, and d4s for skill level.

Anydice.com helpfully can find the chances of any given number of successes (number of max-value die shown) with:

output [count 6 in Xd6] + [count 4 in Yd4]

So far, so good.

What Im trying to figure out is how do I find the odds that one person will beat (equal or greater number of successes) another person in a contest between two of these rolls with different X and Y values for each person.

Is this doable on anydice.com?

Thank you