The only times I've converted United miles were when there was no penalty to do so:
- UA->Diners->BA when miles converted 1 to 1 because of Diners double BA mile promotion.
- UA->Hilton double point promotion offered about 5 years ago.

Right now, you will incur a huge penalty for converting the miles (through Hilton). As Randy states, maintain both accounts and get added flexibility when you want to book award travel. The only downside is not being able to upgrade your AA paid flights using your UA miles.