I'm not trying to create controversy, but I've read a lot about how a Heavy Bolter with Metal Storm Bolts is totally the sick-nasty against Hordes. I crunched some numbers, and the Heavy Flamer isn't doing bad at all by comparison. Which is to say it is better. I'm not great at math, but bear with me.
For the sake of my this example, I assumed two Devastator Marines with the Horde-killing special ability from their Specialization, and the Mighty Shot Talent. The one with the Heavy Bolter has purchased his first BS Advance, and the one with the Heavy Flamer has Cleanse & Purify. They are both starting characters. The targets will be assumed to be Hordes of some kind of minion with a total Toughness Bonus + Armor Rating of 16.
If the Marine with the Heavy Bolter hits a horde ten times, and can easily damage the Horde with 2D10+10 (Tearing, pen 4), he will deal 20+1D5 damage to the Horde. He hits between zero (as unlikely as that is) and ten times, dealing up to 25 damage. The average number of hits depends on various factors, such as the size of the Horde and the Marine's actual BS... which makes it a little beyond my ability to figure out. But that's the best result. Each hit counts as two hits, and 1D5 is added to the final damage.
The Marine with the Heavy Flamer will automatically hit 8+2D5 times, and if he can easily damage the Horde with 2D10+8 (pen 6), each successful hit will deal 2 damage to the Horde. He hits between ten and 18 times, dealing up to 36 damage. If he gets an average number of hits (roughly 13), he will deal 26 damage.
The way it looks to me is that the Heavy Flamer has a higher minimum and peak damage than the Heavy Bolter. As I said, I don't know about averages. But I think I know what I'm requisitioning the first time I fight some Genestealers.