It looks like they both do the same thing except that blazing hydra damage is a little lower and the damage is delayed by 3 seconds.
Looks like arcane hydra win.
On paper, Blazing Hydra seems to lose out to Arcane Hydra as it does less damage and requires a longer period to do so. However, there are a few situations where you'd be using it:
In case you are wondering why blazing hydra over mammoth hydra, the reason is because the 130% weapon damage is per head/shot, so all 3 added together can total 390% weapon damage, which is far more than mammoth hydra (but mammoth can potentially affect more monsters).