In general, we haven't had problems with above counter sinks. Of course, the larger the sink the less splash problems. A small sink that would be fine for handwashing in a guest powder room would not work well for a master bath where shaving, face washing, etc. occur.

The water stays inside the vessel sink as well as an undermount sink I think.

I personally loathe vessel sinks because I always manage to splash/drip water around while reaching for the shaving cream & razor, etc. and hairs from trimming my beard get everywhere. I much prefer undermount sinks as water & hairs can be swept off the counter into the sink and down the drain easily.

The only above mount type sink I haven't had a problem using was the Kohler Purust Wading Pool because it was so incredibly vast - tho I imagine over long term use and without a maid, I would still manage to make a mess of it.