Costs more money to buy HE detergent with less benefit to show for it I think, but otherwise I don't think it really matters much. I've used it when there was a great sale.
It's fine to use them in a regular washer. They suds less than regular detergents, which is a good thing for the front loaders. It's not good to use regular detergents in the HE machines, but it's ok vice-versa.
There is no DAMAGE from using HE in non-HE equipment.
Monitor your results - you may need to use a little more HE in non-HE equipment to get the same results.