I like lots about TtS too. It's got some really interesting and refreshing mechanisms based on the author reading the original source materials and NOT simply assuming the accepted wargaming myths are correct. It also (mostly) puts the player firmly in the general's saddle, and dispenses with the tactical minutiae that the CinC would not care about, and yet keeps it interesting, with lots of decision points.
And yet I had more fun playing FKP, and I think the answer is sadly quite subjective and perhaps not terribly helpful to you blacksoilbill.
I've dabbled with lots of ancient rules, but my group tends to always come back to a ruleset we really like. DBA, if you must know. Call it inertia, or a bunch of old fogies, but we know it and like it. Especially the latest version, and especially BBDBA. Great fun.
But being an inveterate rules collector, as is one of my friends, we often will try another ancients set. And almost always, after the battle, we shrug and say "meh" at best and conclude DBA is more fun for us.
Almost always; for the record, we felt TtS was a lot of fun. We didn't think it was better, but we'd absolutely play it again, which we did and is quite rare for us. It's a different flavour – like vanilla and chocolate. One isn't better than the other, but they are different yet equally good.
But when it comes to renaissance warfare, we tend to play DBR, which is OK. (And not just ECW – we've got lots of armies in many other wars and periods). I do have fun playing it, but somehow sometimes it doesn't feel quite right. So we've tried some other rules, but they also just don't feel right.
Long story short – I at any rate, felt FKP was indeed better than DBR. Maybe it's because I don't have an automatic "goto" set of rules for ECW that everything must be measured against unlike ancients.
As for specifics, nothing really leaps to mind. Well, in TtS I have some reservations about the way elephants and scythed chariots are handled, and sometimes the scale bothers me a bit. The shooting ranges seem much too great for me, and together with the elephant rampaging rules seem much too tactical for a ruleset that justly prides itself on allowing you to command an army. (And once more I stress that these points are mere nitpicking; as mentioned I'll happily play these rules again).
But I felt none of that in FKP. Smaller armies, smaller actions for one. I loved the way shooting has changed to reflect the rise of gunpowder. Overall – and again, totally subjective – it just "felt" like an ECW action to me.