what type of flats your getting, punctures or pinch flats. If it's puncture flats then neither system is gonna help much. You can puncture a DH tube or a UST tire just as eaily as anything else. It just takes a bit longer thorn to do in a DH tube. The better solution for puncture resistance is UST with sealant. UST tires do have a bit more puncture resistance than a "normal" tire. But it is a bit of a pain as the sealant needs to be "refreshed" every two to six months or it tends to dry out and become useless. And if you change tires often it's an even bigger pain.
As for pinch flats. DH tubes to resist pinch flatting better than standard tubes. However you can still pinch em if you're running low enough pressures. That's probably the biggest advantage of running tubeless. As long as you run reasonable pressures the system virutally eliminates pinch flats. Run em too low though and you will pinch the sidewall of the tire and puncture it.
Like I said, just depends on what type of flats your getting. My personal favorite is tubeless. I've had 0 flats in over two years both with UST and regular tires. That and a tubeless tire set up feels different. It's hard to describe, the tubeless set up feels like it pedals lighter even though it may weight the same as a regular tubed set up.