Double spend / bitcoin Bots
Unless we can see exactly where the bots are operating and exactly how the propagate their transactions, we'll never know exactly how one bot wins over another on addresses where the private key is known. However, we can guess on how they win:


These bots are run by miners. As soon as they get a transaction that outputs to a known address, they immediately create a transaction that spends the output to one of their addresses. If they happen to mine that block, the output is theirs. If not, they can still propagate the transaction and hope to get the output anyway.
The bots run on really well-connected nodes. Multiple bots spending the same output is essentially a double-spend. In a double-spending situation, the better connected and faster propagating will win (in the absence of the above). It's possible someone has direct connections to the most well connected nodes and can propagate such transactions very quickly.


My guess is on #1, though it's hard to say for sure. If it is #2, it's possible it's a well known website like blockchain.info.

Basically, we're speculating, but you, as an independent node without any special relationships to miners or large nodes, stand no chance of winning over either #1 or #2.