To me it looks like many people think of classes (and/or equipment) quite backwards. I think it might be going on in big, commercial AAA games too to some extent, hence the bad experiences people have had with class systems.
I think that classes, and all weapons/equipment/whatever must enable certain, carefully considered gameplay. For example, if you want the gameplay to include a superior ability to kill enemies with great certainty from far away, sure thing, consider adding a sniper class or a selectable sniper rifle. But ONLY if you really want to enable that kind of gameplay and think it will make the overall game more fun!
I think it's a great error to add (for example) a sniper class/rifle just for the sake of it, and only then start to wonder how it could be made to fit into the gameplay you have or are going for. This is how silly classes/equipment and balancing issues come to be.
From gameplay's perspective, it's actually irrelevant if a feature is implemented as a class or a piece of equipment. The implementation is just a means to an end (the gameplay). Try to look beyond classes, equipment and whatever, and look into the gameplay that the class or equipment would bring with it.
For Running with Rifles, I would go with selectable equipment. To me classes would imply visually different character models (think of Team Fortress 2), and I think the production would be better off with avoiding that extra content work. The RWR characters are these generic, jolly soldier guys anyway, so just expand on the current idea of giving them sticks that go different kinds of boom!
