I dont know much about the TK20 but I have the LD10 as EDC (always in my inner pocket when I am out). The LD10 is very nice and I am quite happy with it. I am using Energizer Ultimate Lithium as for now. Dont have much need for rechargeables at the moment but Eneloops gets alot of good response from other users.
Im sure you will be happy with both of your lights
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.