The two methods
Both methods pay the minimum on every debt, every month. The difference is where the extra goes.
Avalanche puts every spare dollar on the debt with the highest interest rate. When it's gone, that debt's minimum payment rolls onto the next highest. It always costs the least interest. That's just math.
Snowball puts every spare dollar on the smallest balance first, whatever its rate. You clear a debt sooner, which feels like progress, and the freed payment rolls onto the next smallest.
The honest answer
Avalanche is cheaper. Snowball is easier to stick to for some people, and a plan you stick to beats a cheaper plan you give up on in month three. This calculator shows you exactly how much the easier path costs, so you can decide with the number in front of you rather than on a feeling.
Where the mortgage fits
Leave the home loan out of this list. At 6% it's almost certainly your cheapest debt, and card debt at 20% costs more than three times as much per dollar. Clear the expensive debts first, then send everything that was going to them onto the mortgage.
Buy now, pay later
These usually charge no interest if you pay on time, so avalanche puts them last. Late fees aren't included here. If you're paying late fees, count them as the most expensive debt you have.