If you had to choose between the two, who would you pick and why?

For solo runs, Splinter. For co-op, with 3 or more players there should always be a Don or Casey for their standing super. With 2 players or fewer, Splinter.

Splinter may theoretically save slight time on bosses, but the collective amount of time that Casey's super saves on screen clears across the entire run definitely makes him more valuable in a co-op run. Theoretically the same should apply in solo runs, but I think there's enough room for improvement on both characters that only time will tell!