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are heavy flamers better than heavy bolters

It really depends on the army. For imperial guard I like having them only on hull mounts. Veterans are better to have all 3 melta or plasma. All have their places in an army. Though I'm talking mostly from experience with guardsmen.

Depends. Same S and Ap values, and HF's do not need to roll to hit. However, HB's have about 4x the range of a HF.

If we're talking BS3, I would say the heavy flamer. You will get as many wounds with a single shot of the heavy flamer (assuming you can tag 4-5 models) as a heavy bolter would over the course of three turns. Then there's the whole cover-ignoring bit.

HF is great for chimeras. HB good for say a hydra that needs all the shots it can get

Heavy Flamers, if you can get out of trouble as quick as you got into it.

Yes, the heavy flamer is always better, with a few exceptions. One of them is that it's worth having a couple in a gunline (which itself isn't worth taking), and another is if you have one of those peculiar vehicles where a hull heavy bolter actually matches the vehicle's primary weapon (such as a hydra or exterminator).

Otherwise, you're going to want to be moving anyways, so you might as well take the weapon that is far better with every respect other than it takes movement to use.