OpenTransactions is a system of federated servers that manage IOUs in a way that you can prove your balance with the server. If I had to state the single biggest flaw with OT it would be its dependence on the legal system to 'punish' cheaters as it does not prevent cheating, it only makes it hard to do so without getting caught.
IMO it's a mistake to think of Open-Transactions as being in competition with any chain-based system. OT is more likely to be used with BitShares, rather than as some form of competition against them, as should be obvious to anyone who views the videos that were posted in this thread.
That said, I feel it necessary to point out a few things about OT to make it clear that OT is dependent on cryptographic protocols, not on the legal system.
First, OT is unable to forge your receipts. This is because the client-side forms the receipts, and the server only counter-signs them. Furthermore, the current account balance is on the receipt. Therefore the client will never have to worry about a changed balance, or falsified receipt, because the server does not have the client's private key.
Second, any blockchain-based currencies used in OT, such as Bitcoin, will be stored in multi-sig voting pools on the blockchain, which makes it impossible for any OT server to steal any Bitcoins that users are transacting on that server.
So right there, the OT server cannot forge your transactions, cannot change your balance, and cannot steal your coins. This is without any need of legal intervention, since it's based on public-key cryptography.
The only possible crime left would be inflation. However, the voting pools protocol fixes this as well, because all OT servers in a given voting pool perform real-time audits on the receipts from the other OT servers in that pool. (They have an incentive to do this because users have the power to move their funds between the servers in the pool, and to withdraw their funds from the pool even without the permission of the server being used.)
Therefore OT is not built based on some legal dependency.
There is still one vulnerability left: If, say, 18 out of 20 servers in the pool collude, they can steal all the coins in the pool. We do not deceive ourselves that we can completely eliminate risk -- OT's philosophy is more based on the effective distribution of risk. Even Bitcoin itself does not eliminate risk entirely, but merely distributes it effectively so as to make it secure for all practical purposes. Since OT is client-centric, the next level is to distribute funds across multiple pools, at the client level.
In sum, to those who think of OT as some form of competition to BitShares, understand they are completely different technologies and likely will be used together -- neither will replace the other. And to those who believe that OT is based on the legal system, I assure you it is not. OT aims to eliminate the need for any legal system by replacing it with cryptographic protocols.