First, I'm not trying to pick on you, I'm just using this as an example.In this case what you'd need to do is record how many times you're "recovering a par" compared to how many times you miss a ~30' putt to see what's more beneficial. If the putting only gets you one or two strokes per round, but you're "recovering" a par 5 or 6 times per round then driving is more important. If it's the other way, than putting is more important.
The thing is people rarely have actual recorded numbers, so no one actually knows what's more important for any given golfer. It's just a bunch of speculation.
The problem comes with definitively saying whether or not a drive actually cost you an "extra" stroke on the scorecard. When you miss a putt, that's guaranteeing at least one extra shot you otherwise wouldn't have had to throw. It's easy to quantify that. You can't really do the same after every "bad" drive in a round. Unless you ace, you are always going to have to make another throw after the tee shot.
It's easy for me to look back at my last round and see that I missed 6 putts within 25 feet, one of which rolled away downhill and I needed to two shots to finish that hole. So that's up to 7 extra strokes on my score that could have been prevented by making more of my <25 footers.
But looking at my less than ideal drives in that same round is tougher. I missed four drives where, in my estimation, a good/great drive would have put me in the circle. On those holes I took two 4s (including an OB) and two 3s. Do I count that as costing me two extra strokes (the 4s not being 3s)? Or should I be assuming a good drive = a deuce so I could/should have been four throws better?
I also had two tee shots that came up well short of my intention, but they were both on multi-shot holes so regardless of how well they were thrown, they weren't reaching the circle. They just both meant longer approaches, which I executed just as well as I think I would have if I'd been closer. So IMO, neither drive hurt my score even though I'd classify them as poor or misses.
This leads me to think it would be easier to improve my putting to improve my score. It's just much more definitive in its effect on my overall score. That shouldn't diminish the need for making good tee shots, but if you can't finish them off, what good are they, really?