Don't know about Holyhead never fished it but I would choose Anglesey over Bridlington any day.That many places to fish no matter what the conditions, there is always somewhere on Anglesey that will be sheltered from the prevailing winds.
I live near Bridlington and fish the Holderness coast on a regular basis. I’ve not fished Holyhead for a few years but would agree with tdxs. Holyhead / Anglesey would get my vote.
Summer fishing Bridlington South pier (fish dock pier) gives you the chance of a few school bass, thornback ray, dabs & flounders + the chance of a few mackerel dependent on the weather and if you can get the choice spots on the pier.