It made absolutely no sense to me to buy a splitter that would take 4X the time to split the wood, just in case I found a gnarly stump.
Horses for courses. If don't see much ugly stuff, or can afford to pass on it, then a kinetic splitter is the ducks nuts, given the budget we are working to in this thread.
That said, if lots of uglies or really difficult wood, or just don't fancy having a 'leave pile' of uglies not worth the time of day to split, then a hydraulic would be the go. There are some fantastic ones I would suggest if the OP's budget could be increased to around the $5k mark.
I also don't want to give the wrong impression that kinetics can't handle ugly wood. They, with a good operator, can split anything you can put on the table, but often it's a real PITA and takes multiple hits and tiring wrangling of wood back to the knife to be resplit down to smaller sizes. There are mods to help in that regard, but if I had lots of uglies I had to split rather than leave or re-purpose, I'd choose a good hydraulic (new or used) if money were no object.
But, under $3k and already owning a chainsaw, a kinetic is hard to beat.
Also, even though it was an early picture and you have probably worked this out by now, in case others haven't, try splitting up the tree, not down it, i.e. turn that round around so the top of the tree is facing the operator and the bottom of the tree is facing the knife. Not always possible, but for these types of knives, it generally takes less effort and leaves a cleaner split and less trash wood.
I believe someone owes you $100.
As for what's most productive, there's lots of variable here. Final split sizes needed, size of rounds, etc. A case could be built for either and both splitter types in certain situations.
If money no object, lots of variable wood (think arborist cast-offs or general bigguns nobody else wants to mess with, or uglies as value added firewood operation alongside a mill), I'd be buying a monster hydraulic and pushing rounds through a box wedge. No re-splits, but a ton of scrap wood to deal with.