There's a difference between high and low profile tires in the sand.
Biggest difference...tire pressure.
Higher pressures allow you to have more control in the sand, while lower pressures give you more traction.
A small wheel benefits more from low pressure because the footprint spreads out more, and at the same time a higher pressure will make the tire balloon and appear rounded at the footprint...meaning it won't float well and has a tendency to dig in deeper which can rob power.
A large wheel benefits from higher pressures because it allows the tire to maintain a flatter shape and stiffer structure for handling, while low pressures are very detrimental to the tire since there's very little rubber between the ground and the wheel.
If you drop pressure too much with a big wheel, the tire is more likely to pop a bead and cause damage to the wheel...landing a jump on a hard surface or hitting a big enough bump can deform the wheel.
Likewise, a small wheel with low psi has more cushion and the tire itself gives as opposed to translating that force to the bead area, but at the same time it exposes more of the sidewall to damage and can cause handling problems.
Your terrain and riding style determines what size wheel you should use.
If you ride fast or race in the dunes, go with a big wheel and higher psi.
If you hill shoot or jump in the dunes, or for all-around performance, go with a small wheel...pressure is further determined by how much air you get and how often...bigger jumps, more psi, fewer jumps and cruising, less psi.
I've had both, and much prefer small wheels with big tires and just enough pressure to manage some decent jumps without ballooning the tires out.
Big wheels are great for high speed level sand, but they'll wear you out in choppy sand for all those times you're not screaming in top gear in smooth sand (shocks help, but don't fix the problem).
Regardless, it's not always a matter of wheel size and psi, sometimes it's a combination of those along with total weight, construction of the tire, and numerous other factors that all go into what type of setup is best tuned for you, the quad, and the terrain you ride at.
Tuning all of these factors in is what makes the most enjoyable, capable, or successful quad out there...you can have an awesome quad and rider but lose the race because the wheel setup wasn't right.
It's a lot of work, takes a lot of time and money to figure out the perfect combo, but that's why people build quads...it's their hobby.