Use what ever the cows are use to. If they are use to being on foot... be on foot... if they are use to horses... use horses... if they are use to pink barbie jeeps... use pink barbie jeeps.
Being horseback gives some people a false sense of security. When your horse gets thrown out of the working pens you will think twice about being horseback.
Especially with Brahman cross cattle always ask how they work them and insist on getting in a pen with them on foot if that how you plan to work them. Walk behind them and make sure they will turn their butt to you and walk away. Look for high heads right when you step foot in the pen. Make sure they dont square up to you and try to do that backing mess while looking at you. See how big their flight zone is.. no flight zone is just as bad as a huge flight zone.
That all goes back to buying cattle from operations who operate like you do... or in my case... where I want to be.
Never have found anything false about the security of being horse back myself. And, I never met the cow or bull yet that could throw one of my horses out of a pen!! Maybe 50 years ago I might could climb or jump up on a corral panel to get away from a cow, but not now. I have, however, ran over a bovine or two that had someone pinned down or against something before. Stomp their ass one good time with your horse, and they will learn to respect them right quick.
One of my favorite cow ponies ever was a Mr. Gunsmoke stallion I had in the 80's and early 90's. One summer I was riding through the pasture with my helper in the truck, to go work on the fence in the back of the place. Saw a Braford cow stranding over something that I figured was a calf ( a surprise calf that time of year). Rode up close to it, and she took off all snorty and wild-eyed, with the calf trying to keep up. I saw where he had skinned his back in several places, and the flies were blowing it. I went to the barn, and got the stuff I needed to treat it, saddled up Smoke, and told my helper to follow me in my truck. His border collie/Aussie shephard jumped it and went too. Well, got back out to the bitch, and she took off like a bat out of hell, with that calf right on her heels. We came to a barb wire cross fence and she sailed over it flat-footed, and I heeled the calf right about the time he tried to jump through. His front legs got twisted between the bottom and next to the bottom strand, and I got off the tend to him. Smoke was working the rope good, and had it a little too tight for me to get the calves legs out. Calf bellowed like I was killing it, and here came Momma back over the fence, and tried to get in my pocket. Helper jumped out of the truck, got a fence post out of the back, and busted her in the face with it , as she ran over him and never slowed down. LOL. Dog jumped out and got in front of her, and she planted him too. I finally got the calves legs out about the time the cow got to me. When Smoke realized it was free, he spun around and got down cutting that cow better than any WGC I ever saw in Augusta. He was popping his teeth and snaking his head at her, trying his damndest to bite her. When she backed off a little. he turned his ass to her and went to backing her across the pasture, kicking the ever-loving daylights out of her. I put the calf in the back of the truck, and loaded what was left of the dog and my helper in too, and doctored the calf from there. Smoke wouldn't let that cow within 50 feet of the truck. Had we been on foot, the cow would have hurt us. Well, if I didn't have the horse, never could have caught that calf that day anyway.
I realize that everyone with cattle can't use horses, for several reasons; Can't afford them, dunno how to use them, don't have the pasture, hay etc for them. And I found out a long time ago, that you can teach a horseman to be a cattlemen, a HELL of a lot easier than you can teach a cow farmer to be a horseman!
I have seen cattle that you couldn't get in a pen on foot with, for sure. But never seen any of these yet that I couldn't settle down to using a horse with them. Never seen cattle though, that you couldn't work with a horse...if the facilities are built for working cattle... that you could safely work on foot.
But to get back to the original discussion, I have found that Brahmas and Brahma crosses are no harder or no easier than any other breed to handle. I think they are like pit bulls...people tend to be scared of how they look. However, cocker spaniels account for more dog bites than pits do.