I think in Escape, the Brawler card isn’t that essential generally. If your Venom Blade is high enough, then the bleed will just do the work and kill most Drone sized enemies without Brawler. Hit and run attacks will work just fine. Sometimes I prefer to use the Short-range Deflection card instead of Brawler.
However there are some situations where Brawler is very useful as you want the enemies to die ASAP rather than wait within an extra second for the bleed to do its work. The Warren for example, has Juvies with melee-resistance and there’s lots of them, so you probably want them to die quick.
In Horde, your venom cards are redundant as there’s no venom, so you instantly have two slots freed up (Venom Resistance and Venom Blade) for other things. Plus in Horde on higher difficulties, you have the initial x2 enemy health mutator; and from waves 11 and 41 there’s an extra 2x and 0.5x added on, so in total you’re dealing with up to 4.5x extra enemy health compared to 2x in Escape so you will probably want that extra damage.