I think everyone who plans a trip to Cape York agonises over this same question

Do you specifically want to stay at Loyalty Beach or Seisia, or are you open to more options, and hence a bigger decision making headache?

We ended up camping at Punsand Bay, Alau Beach, and Loyalty Beach, and stayed in a cabins at Seisia and at Resort Bamaga on our trip last year.
I've listed them there in order of what I thought was least formal/caravan park like to most formal/caravan park like, or most bush like to most civilised.
Punsand Bay is under new management this year, and they've apparently done an overhaul on the place. They've even got beer on tap now @ $5/schooner.
The new managers are supposed to be very good operators(they run the Cape Tribulation Camping Ground).
We loved it up there, and the kids loved the pool too. Magic sunrise and sunsets and beautiful sandy beach.
It was the least caravan parky of the lot (last year). As mentioned before, the unpowered sites are towards the beachfront, and the powered sites are near the back.
If you don't like bush camping though, you won't enjoy Punsand Bay as much as the others.
Alau Beach (at Umagico) was a welcome surprise, with nice clean facilities and a beautiful beach. It was less touristy and had more of a local Cape feel. You have to weave your way down through the community of Umagico to get to the beach, and it is the smallest of the parks up there, but we really enjoyed our one night there, and would happily go back for several nights next time.
Punsand Bay was our favourite, followed closely by Alau Beach. They seemed to have more character about them than the others.
If you need a campsite with all the amenities close to town, then my personal preference out of Loyalty or Seisia would be Loyalty Beach. Seisia was very,very popular when we were up there in July. The good thing about Seisia though is that you can walk to the shops, wharf and fishing club etc....
In the end, I think you need to consider where you'll be spending the majority of your time: around the campground and town relaxing and socialising, or out sightseeing and exploring? Also whether you're caravan park people or more bush camping, with amenities, kind of people?
Here's a link to some photos of our campsites if you want to get an idea of what some of them are like. They start at the end of page 6 (Alau Beach) and go onwards.
They may give you a bit of an idea of what the sites and beaches are like.
http://www.myswag.org/index.php?topic=25497.0Odds are you'll enjoy whichever one you pick

Cheers
Karen