I have more experience with this than I'd like.
Crossbow is a Dow product, it's triclopyr and 2,4-D plus a surfactant that helps it stick to leaves that have waxy surfaces (like blackberry).
Roundup is glyphosate. Some varieties include a surfactant, too. My experience is that the surfactant helps a lot.
Anything with those active ingredients in the right proportions will work just as well, but some of the cheaper alternatives lack surfactants.
For blackberries and salmonberries, timing counts for a great deal, in particular if you spray early in the year you'll seem to have won but it will spring back with a vengeance next spring.
I've had very good success with tackling large patches in early fall, after the berries are gone and just before you think the leaves are going to start to turn. Spray it all at the *recommended* rate. If you use too much, you'll just burn the leaves and not actually kill the roots. Then, a week later, go around and spray again. Wait until the effect is really apparent, then mow the canes right down to the ground with a brushcutter.