Aesthetics and construction aside, F-hole mandolins will typically offer a brighter tone, with more volume and a stronger attack. Sometimes, they can offer a slightly more percussive sound, depending on the instrument.
Oval hole mandolins will usually have a warmer, more woody tone and offer greater projection, sustain and resonance - particularly in the lower register. The higher the quality of the craftsmanship however, the fewer the differences that exist between the two styles.
Traditionally, oval hole mandolins are more commonly used for traditional Irish music and folk music, while F-hole mandolins are played in bluegrass, country, and folk rock.
This is not a hard and fast rule however. You can play any style of music on whichever style of mandolin you prefer.