I have both the L1T and the P1.
The P1 has higher output but uses special lithium CR123 batteries, sold in stores for $7+ each. Online, however, CR123's can be had for $1-2 each. It also has one level of light output, but as it runs for two hours on a single battery, runtime isn't all that much of an issue. The size of the P1 is great and it hides easily in the right front watch pocket of my jeans. It's small size and excellent light output also makes for a great "showoff" light, as many cannot believe how much light comes out of the tiny thing. If you get rechargeable 3.7v RCR123 Lithium Ion batteries, you can run the P1 for about 30-40 minutes and it's about 20-30% brighter, but it also gets very hot.
On the other hand the L1T is less bright but offers two modes of output -- high and low. On high it will run for about three hours, and on low it would be great for blackouts and camping, as it is still pretty bright and runs for around 10 hours. It'll also take a single AA battery, which makes it great for travel -- you'll never have to hunt around for special, expensive batteries, and it's cheaper to run. Not only that, but you can later buy an L2T spare body from Fenix-Store.com and run it on 2 AA's, making it comparable in brightness to the P1.
I don't really consider either light to be better, as each has their own distinct advantage and I like both quite a bit. I really like the CR123 format but it is not for everyone and using exotic cells can add up to be quite expensive in time. Both are great EDC lights and which light you choose should be up to what light you think better suits your needs, as both are small enough to easily slip into a jeans pocket.