I like the old-school Roundup concentrate or the generic concentrate. Takes a week to do its work, but when its dead, it ain't coming back this side of an act from God.
I mix as directed, but include a healthy amount of surfactant, meaning, I buy a bottle of cheap pink dish soap or laundry detergent and add some into the mix. Usually 1 cup/gallon of mix. Much, much more effective than than just herbicide concentrate & water.
Woody stuff will take a very high concentration or you'll have to use something else that would outrage the enviros(0). Also, some vines & ground cover are resistant. My neighbor's asian jasmine requires similarly high concentrations.
(0) Diesel fuel