Drop bars can easily be strong enough - but they're usually engineered for road use, not engineered as strong as MTB bars. However, cyclocross bikes use drop bars, which are just fine. Make sure you use the correct sort of stem, etc.

Main loss with drop bars is they're not as wide, so don't give as much control with tricky steering. BUt I'd say, if your bars are strong and in good shape (and not flexy like Modolo bars), go for it.