I don't use them for competing, but we have a pony at the barn who is much happier and settled when he has them in- there's less info he has to process and his mind can be calmer. Sometimes their minds just move too fast and taking away the stimulus of hearing can help them relax.
POMMS are a great brand, very comfy for the horse. Make sure you push them pretty far down in the ear or they will pop out
Ear plugs can be a useful tool, but they usually indicate a hole in a horses' training. If you've done your due diligence and brought your horse off property, and exposed them to new situations, they should be able to settle down relatively quickly at a show without ear plugs. There are brands you can use, but I know people who have used cat toys from the dollar store instead. Just a similar size and shape, any ball shaped toy that is the same size will do the trick.
I had never used it and then one day I was told about POMMS Premium Equine Ear Plugs, and I tried them to make my personal opinion.
I find it very good especially for people who can not concentrate with noise around them (which is not my case). I think it's a good idea to have done this for the riders. This is my point of view, but I prefer not to put ear plugs because I do not hear 100% my horse and I prefer when I can hear it :)
Have a good day,