First of all, lets get some things straight. Putting does not automatically win tourneys. I played a tournament and only missed one putt inside of 30' and still finished 16th out of 27 for the intermediate division. Unfortunately, the one I missed hit chains and fell out on my only birdie attempt that day from inside the circle.
My drives were half the time just 50-60 feet out, hit a tree, or the basket was over 400 feet out. My second shots were inconsistent as well with some great shots and then some that put me in jump putting distance (my jump putting didn't work that day). The weather wasn't cooperative, either, with big wind gusts and random rain throughout the day. I shouldn't use that as an excuse, though, because my disc selection was poor on some shots.
My point is that just great putting doesn't make you competitive. Good control on your drives and solid approaches will make you competitive. Once you have that down, putting will only push you to the top or drop you down.
I think solid driving and approaches is more important than putting. I have been practicing my putting almost every day and I am now a great putter. I have noticed my scores have been stagnating or even getting worse by a stroke or two lately. The reason is that my putting has been hiding my bad drives and approaches because I have been hitting almost all the 20 to 30 footers that come around.
I think that before you really concentrate on your putting, you should concentrate on getting your drives consistent. That doesn't mean you shouldn't practice putting, but you should put more time into driving until you get to the point where your putting practice can pay divendends. That is why I started putting more effort into controlling my drives so I can use my putting for birdies instead of saving pars.