I found this line in the source:
https://github.com/ondrejduchon/TreeChopper/blob/master/src/main/java/treechopper/proxy/CommonProxy.java#L119
which means that an axe takes durability damage of 1.5 times the logs chopped, even if it is enchanted with Unbreaking III. I don't mind the basic idea of it costing more durability to chop the tree down all at once, but:

1. This is undocumented behavior.
2. Making this multiplier be configurable might be better.
   and most importantly:
3. This should be relative to how much durability the axe would normally lose in consideration of enchantments (and possibly power usage if the axe is from a tech mod), not simply based on the number of logs chopped. Thus an unenchanted diamond axe chopping 80 logs at once would lose 120 durability (which it does currently), but an axe with Unbreaking III would only lose about 30 durability (compared to about 20 using such an axe to chop that many logs one at a time)