I enter various writing competitions (including those run by festivals) and, where there is an opportunity to have feedback, I usually opt for this. It involves an extra fee (to pay for the judge's time). My criteria for whether I go ahead or not depends on who the judge is, and the fee.
I judge if the fee is worth it by, again, who the judge is (I'd expect to pay more for a "name") and most competitions will give you an idea of what you can expect in the way of feedback.
For example, a novel judging competition I would expect to pay a significant fee (in the UK, at least £25), given the amount of time involved in reading and assessing a book. I would also expect a good sized report for that money.
For a short story, I would expect to pay a lot less and would expect to have comments on a sheet of A4, maybe two, depending on the length of the short story.
It pays to keep an eye out on what different competitions and festivals charge here so you can get a gauge for what's going on "in the market". If in any doubt about a competition, check it out with a reputable writing body such as, in the UK, the Society of Authors. I enter competitions I know about through publications like Writing Magazine, recommendations from fellow authors via FB etc, and those that have a long history (easy to check out on websites etc).