I am assuming you mean a turboprop vs jet.
There are more thing that can go wrong with a turboprop, like prop pitch control, synchronization, mechanical linkage, fluid levels, etc. A vast majority of engine shutdowns that we have are due to prop related issues.
As is usually the case, the less complex, the safer and more reliable. Compared to a piston engine, the jet will run as long as it has airflow and fuel. A jet is shut off by stopping fuel flow.
Of course, most of this is more about reliability. Properly maintained engines, no matter what kind, are safe.
ADDED: Unbelievably, when you look at a C-130 intake duct, it's hard to imagine that birds can get in there past the prop, but they do. Our problem here in Georgia are the buzzards.