The TK20 is great outdoors, best in a forest. The warm tint makes things more 3-dimensional. The 150 Lumen don't sound that much compared to the 240 of a TK11, but in a forest you're better off with the TK20.
I use it often in combo with the L2D, mostly I don't need the second one. I don't own an LD10 yet, but I have the L1D which should be comparable. It easily fits in a pocket, quite bright. I'll give it to my mother soon when my LD10 arrives...
I suggest rechargeables, depending on how often you ue them some with low self discharge. Just carry some spares.
Have fun with the lights!