The edges you get from both are fairly close. In fine grits, I think the arkansas stone produces a finer more even edge.
Diamond stones cut the steel faster. But this makes them a little trickier to get the hang of. Don't practice with them on a good knife. Use a junker. When you understand how they cut and can produce an edge you like, you can move on to other knives with less fear of destruction.
I carry a two grit diamond hone in my outdoor gear because it is light and small. Around the house, I only use diamond hones when I have an edge that needs a LOT of work. I'll do the major work on diamond and finish on ceramics or arkansas for the final edge.
If I know I'm going to be working in tough fibrous material I sometimes take a stroke or two on each side of the knife with a medium or maybe fine diamond hone. The consensus among knife knuts is that diamonds produce a somewhat toothy edge, sort of a micro serration pattern. that helps you cut through tough fibrous stuff such as rope, cardboard, fabric, plant matter and so on.
Diamond hones can clog faster in my opinion. Probably because they aren't naturally porous materials and cut so fast, the swarf builds up quickly. Rinse and brush under running water. Dry thoroughly so any remaining swarf doesn't rust and gum up your hone.