I would say it depends on what you're doing.
The thicker bottomed pots & pans will store a greater amount of heat, and thus won't cool down too much when trying to sear or fry something. If they do cool down, it takes a long time to come back to temp due to alcohol's lower heat output.
If you're heating bulk quantities of liquids, I don't think it would make any appreciable difference. For small quantities, it would make it take longer.
We have an all-stainless, heavy-bottimed nesting cookset, and it has worked out quite well on our Origo unpressurized alcohol stove.