On turbo the P3D will not run as long as the L2D. The P3D may get too hot on a hot day on turbo. Both of those lights recommend only running them on Turbo for ten minutes if it's a hot day. I don't think the L2D will be so hot, this is better for long term LED life. The 123 batteries can be dangerous if not handled properly. The rechargeable AA's are less trouble than the rechargeable 123s. Even though they can be found on line, lots of people don't search well and can't find 123's that are inexpensive, they mistakenly think the price of the local store is how much 123's cost (maybe $12 each). It's not true. But AA's might be easier to find on the road if you need some. Some people may already have rechargeable AA's and an AA charger.
The L2D is not special. But it's a reliable, well made, well thought out product. But, so is the P3D. So are lots of others.