IOTA uses Hashcash in its Proof of Work mechanism, which uses the hash function SHA-1 to prevent spam in the network. The difficulty is currently 14 MWM (e.g. 14 trailing 0's in ternary ?) They say it takes a few minutes on a modern PC. Bitcoin uses a similar approach, but the hash function is SHA-256 and the difficulty is much higher and will probably rise as more specialized hardware joins the network. In both mechanisms a valid hash needs to be brute-forced.
As far as I understand, the PoW in IOTA is currently less expensive than in Bitcoin because its difficulty is not (yet) as high as in Bitcoin. And "a few minutes" is still quite a lot computation power, especially when we are computing on an IoT device. For SHA-1 people could build specialized hardware to create faster transactions (and spam) as well, don't they? So, where is the advantage in IOTA's PoW (as claimed in the docs)?