We're about to battle our Creeping Charlie problem and did some research last night on what to use. From what I read, Ortho Weed-B-Gon Max has worked out the best for others. Creeping Charlie is extremely difficult to get rid of, so I would assume the Ortho would kick the crap out of your weeds.
As far as the vinegar weed killer method...
According to our old neighbor, that method worked, but we nicknamed her "Yard Douche" after she made our backyard reek like Summer's Eve.