Straight grain binding whether long- or cross-grain is just fine. It is definitely faster, easier and you don't need to make as much excess binding.
In general I make bias binding and prefer the french double fold method. I machine sew on front and hand sew the binding down on the back. The bias is mostly helpful when you have curves and such, but I like the way it makes striped fabric march around the quilt. I also feel the diagonal seams are stronger/have less problems and are less noticeable but you can still do that with straight grain binding.