Joe D was more suited to be a ball-handler, Isiah mentioned that he/Dumars/Microwave all split time running the offense and they could all play off the ball pretty well too (though it was mostly Isiah/Dumars as the primary ball-handlers). Dumars was always a good three-point shooter and shooter in general but Klay definitely has the edge. Klay is more apt to go on great scoring runs sometimes and disappear at other times while Dumars was pretty consistent.
Defensively it's closer than a lot of people realize which is why this is a good comparison. Klay is tough and surprisingly quick and often spends a lot of time on point guards. Dumars is highly revered and was a perennial all-D first teamer in his prime and similarly to Klay, you won't find a lot of metrics that'd paint either of them as the defensive stoppers that they are/were. Even though Klay isn't making first teams (I'd give him a pass since his competition is Kawhi/Butler/AB/PG/CP3/Tony Allen), I'd say his defense is at least comparable to Joe's.
Comparing primes it's fairly debatable. Might still give it to Joe because he showed he could elevate his level of play consistently in the playoffs in his prime and can say he was the best player in a Finals series (averaged 27 and 6 on 57% shooting to get his FMVP in '89), but Klay is damn good in his own right and should get some votes.