Suppose you constructed a bitcoin competitor, say bitcoin2, that relied on proof-of-work. Your bitcoin competitor has much less computational power than bitcoin. Any of the bitcoin miners could therefore conquer your tiny network and start reversing transactions whenever they pleased. For this reason, there can only be one. Even if your bitcoin competitor were technologically different than bitcoin, but still relied on proof-of-work, then it could be conquered by any of the bitcoin miners at any time.
there isn't just one kind of proof of work, however. an alternative could require a greater (or lesser, or just different) capital investment than gpus and thus be roughly as secure with more or fewer users. for example, consider one network that relied on a computation that could not easily be sped up with gpus, other asics, or fpgas; there, only cpus would be relevant, whereas gpus and other devices would be relevant to bitcoin. the two could exist in parallel without one being monotonically 'more secure' than the other.
but the more important point remains that '
most secure' is not what's important. a system needs only to be good enough to do what people want it to do. multiple competing currencies could achieve that, even though only one of them is 'most secure'.
I agree that if a decentralized currency didn't rely on proof-of-work then it could compete with bitcoin. But no one has actually invented such a thing, and I suspect that it's not possible.
there are two responses to that. the simpler is that proof of
work isn't necessary; as satoshi recognized, you just need proof of
resources, and he picked work as a judgement call. there are any number of other kinds of resources that could be used. for example, satoshi considered and ruled out ip addresses, but they're not obviously better or worse than cpus or gpus in the steady state. (ip addresses were probably more prone to what would have been perceived as 'manipulation', but then often so are cpus by network administrators, and using computation has many downsides.) there are other resources too, like bandwidth, which is of course the foundation of the emule and bittorrent 'economies'. it could be used in a currency, though it would be more complex to do so.
sheesh. that was what i called the 'simpler' response. the more complex one is that the only feature of decentralisation that requires proof of work is the initial distribution of the currency, though that is perhaps a contentious point. i believe i could show, however, that the block chain's consensus mechanism is not needed merely to prevent double spending; other decentralised technologies could achieve that goal without proof of resources, with whatever probability of correctness was appropriate to a system. (it's all about probabilities; no system to prevent double spending is perfect, including bitcoin's.) the double-spending problem is considerably easier than the question of how to allocate initial wealth without trust, but unfortunately bitcoin uses the same solution for both, thus making the double-spending solution susceptible to more attacks than would otherwise strictly be necessary.