Here's how I see it, your mileage may differ.
If you're already winning (ie. pushing to their towers consistently) priests can help speed things up.
If you're in stalemate, priests are probably not be a good idea, unless you feel that you can use them in coordination with an all-out all-heroes-in-one-lane attac. Even if you manage to rush down a couple of their towers, they rate of their exp/growth will outshadow yours. So if you can't kill them with an alpha strike soon after priests come out, you've put yourself in a disadvantage. An exception to this is if your use or priests allows you to keep the flags. If the flags are powerful enough, it totally offsets the exp/gold increase the enmy gets. Plus, it accelerates the rate at which you can get angels and catas.
If you're losing, and it doesn't look that hopeful, priests can be a last ditch effort. You're already losing, might as well gamble a push.
In general, games tend to be close to stalemate up until the mid section. That's why, from my experience, buying priests is usually a bad idea. There's definately certain situations where it's useful though. The problem with the "noob fruitcake" buying it is that they always seem to buy it for the wrong situation. It's easier to just tell them to never buy it.
Besides, they ought to be buying gold/exp/1st level building health/minion health/attack upgrades instead if they're going to be putting money into the citadel. They're cheap and give huge bang for your buck if you get them early. If you want your minions to push better than theirs, creep health is the way to go.