I think PoB will help with some kinds of 51% attack. For starters, it will mitigate >50% censorship attempts as long as a reasonable amount of PoB'ers are honest. Although the attacker with >50% hashrate can plausibly create a longer chain of PoW blocks and exclude disapproved transactions from them, honest PoB clients will continue to mine burn blocks which include those transactions, so unless the attacker has much greater than 50% hashrate, he will not be able to create a chain that is longer than the sum of ( honest PoW miners difficulty + honest PoB miners difficulty ), which would be required for a successful censorship attack.

In the same way, an attacker with 51% could create a fork from an earlier block to attempt a double-spend, but would require a large proportion of the burnt coins in the network in addition to hashpower in order to get the fork accepted -- otherwise the length of the combined honest ( < 50% hashrate + >> 50% burn ) would always result in a longer (higher-difficulty) chain compared to the dishonest ( > 50% hashrate + << 50% burn ) chain, especially considering the fraudulent chain is starting at some earlier point and has to 'catch up' to the legitimate chain first before it can exceed it.

Finally, regarding the "nothing at stake" problem -- yes, as far as I can tell there's nothing to stop users from collecting PoB blocks on both chains, although this would usually require a deliberate effort to make this happen (since, if they have only a single wallet running, it will fork into one or other of the chains, and not mint PoB on the other one). I can't immediately think of an elegant solution that would discourage this...