TK11 is a Li-Ion 18650 light of the tactical class, with a single-die led,
TK40 is a multi-AA light with a quad-die emitter.
Sure the latter is brighter, but it is also much bigger and needs much more power (thus the added size)
They are a complete other class of lights. Its like You search for a pickup and some friend offers a Porsche, which You like because it can go faster --> is the speed what You want?
I have very often typed my - very personal - thoughs on both lights, and dislike both.
The TK11 is of the useless tactical offering from Fenix. Added edges and teeth and "blings", that only do one thing: make it more difficult to pocket the light.
While this maker once was good, now offers no good 18650 model (and keeps to not offer something for normal users).
TK40 is the same ballpark - strange cell format, strange number of cells, strange inserting (thats what I dislike most)
If You want a light of the power class of TK40, the Jetbeam M1X (and its followers) is WAY better: better batteries, better number of cells, smaller, overall cheaper system cost, more useful technique (f.e. You dont have to recharge 8 cells to run the light, as with the TK40)
if it should be SMALL & still useful runtime, then its single 18650 with single die led.
There are quite some offerings like Jetbeam, Olight w. 18650 body, several others You will read from in here.
one point: 18650 Li-Ion is only available in rechargeable, there is no primary cell to be purchased. When You plan to use a light that could also run with cells You can get in Shop, stay with AA.
PS: when You do not have a charger for AA, and are not forced to use them (for Your GPS f.e.), 18650 Li-Ion is better and cheaper