I'm guessing the second dog may have been an Australian Shepherd from your description.
To answer your question, some dogs DO have very different behavior/play styles than others. Herding dogs can have an aggressive,physical, play style. Since they didn't bite the other dog, it doesn't sound like they planned to attack. Another thing herding dogs do is herd other living creatures- be they other dogs or people. This can involve circling them, nipping, or blocking their movement with their bodies or body language. It can be alarming to other owners who aren't used to it. When I got my shepherd mix he was very mouthy when playing with my Lab (although never made contact), and sometimes rather vocal with growling (but not an aggressive growl, or otherwise showing aggression). He was also VERY intense and physical in his play. I'd never had a dog play like that before and was very worried. I consulted a trainer who said it was 100% normal, some dogs are merely more intense or have different play styles than others.
My guess is, they probably got overly excited and it triggered them to start the behavior, but it could be anything, maybe they've decided that large, brown dogs are things to herd, but small white dogs are not. These dogs are smart and come up with all sorts of quirks like that.
What does concern me is that the owner did not have a leash and obviously didn't have them under voice control. If you're going to walk off leash you should A. by ready to leash immediately if needed, and B. have dogs with a very reliable recall.
As for whether to steer clear or not, I'm not sure. Having not seen the incident, I don't know what I'd do. You might take into account your own dogs personality and how he would respond to such treatment, and also how these dogs seem to interact with other dogs besides the one incident. It certainly wouldn't hurt to keep your dog close when they approach until you get a better feel for the situation.