Are you looking to 'jump ship' prior to the contract award? or are you asking if going to the competition is a good idea if they win the award?
Speaking from an IT contracting POV (not sure if that is where you're at, but some of it may still apply), it's all about relationships. When I was in that space, you can be competing with company B on one contract, and be teaming with them to win another at the same time. In essence, it's a very small world.
There's nothing wrong with switching teams. It happens all the time. You just need to time it correctly. If you're in a re-compete, people may be a bit more sensitive to you jumping to a competitor. Again, that's your decision to make.
Some potential downsides:
- You upset someone who ends up being your program manager down the road.
- You look around, that gets back to your company. They use the contract/re-compete as an excuse to let you go and you don't find another job right away.
- You look around, that gets back to your company. They don't let you go, but try to "manage" you out. You can't find a place to go, so you stay. Now you're even more miserable.
Of course, the up side is that the competitors may actually come looking for you. This is especially if you are a key personnel on the task.