Comparing accuracy of models in ordinal regression / classification
Your classes express a certain order. You can classify apples to, say, "green", "red" or "yellow", and then every disagreement with a reference set is equal. After all, colours express no order. So as you already suggested, I would certainly use regression. Assume that the classes could be distributed as something like this:


Very bad = 0 - 0.25
Bad = 0.25 - 0.50
Good = 0.50 - 0.75
Very good = 0.75 - 1.00


Now, the mismatch of Very good vs. Bad is at least 0.25, where is must be at least 0.50 with Very good vs. Very bad, which gives a better and more honest impression of the performance of your model.