Spray.
Because I said so. (

)
okay, really.
Reason One - because sprays are fairly precise in measuring dosage. One spray for the really strong, two sprays for fairly strong...and so on. With a splash - you're free to use between a dab and cupped palmful, and the results can be disastrous if you mis-judge. Really REALLY bad.
Reason Two - because it allows less oxygen in / through the bottle as the bottle empties. With a spray - you never open the actual reservoir, air seeps in but doesn't circulate through, as happens with a splash bottle that you're constantly opening and closing.
Reason Three - no spills. God help you if you spill a stinky one in your gym bag.
Reason four - no contamination. Say your finger is dirty/oily - that dirt/oil gets into the bottle. You can get around this by using a q-tip or cotton round, but still, inconvenient.
Reason five - easier to decant. If you want to make up a travel size, just spray into the decant container. Have you tried pouring from one bottle to another? Good Lord, it's a disaster. You've got to get equipment which is added hassle.
That's off the top of my head. Most bottles sold today are sprays anyway, so you don't really have much choice in that regard.