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A person doesn't have to throw far to compete,but they better be able to putt,to stay in contention.
Actually, it yields a lot of help on 350' holes. If a 350' hole is a putter or midrange shot you're more likely to be in the circle than if you need a super fast disc to only maybe get there. Putting well only matters if you can get into the circle in a minimum number of shots. If it takes you a drive and an approach to get in the circle for a 350' shot, how is that better than it taking a drive and two putts? What if it's a 600' hole? The driver needs a drive, approach and putt and the putter might need 2 drives an approach and a putt. After two holes the driver is one stroke ahead.
Driving farther does make your shorter drives better. You not only get to use more forgiving and easier to control discs, you have way more options. If you can only get to 350' with two discs in your bag you're at a disadvantage to someone who can get to 350' with all of the discs in their bag.
The thing that many "work on putting not driving" people seem to leave out is that it's much easier to get good at sinking 90% of your 20' putts than it is to learn to throw 450'. Or to put it another way, it's much easier for someone throwing 450' to learn to hit 90% of their 20' putts than it is for someone who sinks 90% of their 20' putts to learn to throw 450'.
Of course the best answer is that you should be good at putting from within the circle and be able to throw far. Which one you should be working on to improve your scores will depend on your current game. The way the question is worded there's no way to know who would be better off.