In regard to "which attribute wins", imo... none of them. Removing the ability to progress naturally through the game and replacing it by a rather turgid and uninspiring skill purchasing model is possibly one of the least exciting things TFP have done with this game.
I honestly thought we had hit a bit of a sweet spot in A16 with a mix of progression and skill purchasing, so I'm sad to see it take what is in my opinion a retrograde step. It seems almost like the skill "tree" has been thrown in at the last minute because, "you know we have to have something and it can't be the same as before".
Now, before the fanbois jump on me, the caveat here is that it's the TFPs game. They've designed it from the bottom up, they've dedicated the last few years to it's development (not without it's rewards, of course) and so if anyone is to be the arbiter of whether it should be purchasing or progression it has to be them. I may not like it, but it's not up to me to like it or not, I am pretty much an irrelevance in this decision. I just hope that it doesn't turn out to be as dull as dishwater as Joel's videos have made it look.
With all that said and done the "winner" is easily Strength (then Agility). Purely on the basis that you spend a lot more time deliberating on your early game. Later games tend to look after themselves. Make the wrong choice early on and those coveted points could be wasted. For example (and I realise it's not a like for like analogy) in A16 you wouldn't start piling points into purchasing the workbench when you don't need it or don't have the availability of the component parts to build it. Those hard earned points would be far better splashed out on weapons or tool smithing. The same will go for A17. It's all fine and well wishing to get better bartering but truth is, if you can't run, jump and hide or hit like a mule then you won't be reaching any trader to barter.
TL;DR?
Strength, but with reservations that purchase > progression is not (imo) the right way to go.