Hi Steph and Sparky, the tape, for me at least, works better for skinny belts, though I suppose you could put several strips on a wide a band.
With the hair elastic, you put your belt through it, like you put the belt through a belt loop, and it becomes another adjustment loop on the belt to secure the end after you buckle it. ( Slide the elastic toward the buckle end. ) You can do the same with a watch strap, if you need another loop to keep the band end down. For skinny belts, you can double the elastic the way you would for a ponytail. You are basically adding a "loop" to your belt to thread the end through. It works beautifully and there are so many hair elastic colors that you can find one to blend right in.
I will post a picture tomorrow for you to "see". It is hard to explain without a visualization.