This is an important characteristic that should be based on how and where you intend to use the trail camera. For example, if you’re primarily handing your camera over a food source then I don’t think camera trigger speed should be the deciding factor when making a purchase. Besides, how fast does a camera have to be to catch a whitetail feeding in a field or over a bait pile? In those instances, the deer are most likely going to hang around for a while before easing off into the distance. Hyper-fast trigger speeds aren’t going to benefit you that much.
However, let’s say you’re hanging your camera over a game trail. Trigger speed suddenly becomes much more important. There’s no doubt deer will be more apt to move quickly through the area; especially if you’re talking about a buck following a hot doe. A slow trigger speed might miss that trailing buck whereas a faster trigger will actually capture him in all of his glory.
So, consider where your camera is going to be placed before paying extra for ultra-fast trigger speed if you don’t really need it. Maybe you do, maybe you don’t.