In my experience with my Surefire L4 and E2DL lights, rechargeables have about 2/3 of the runtime of Surefire or Duracell 123 primaries. My runtime guestimate on the E2DL may be a little off, as I've only had it since Christmas, but I'm pretty certain that it runs for about 35-40 minutes on a pair of AW 3.7v RCR123s. I don't know if a 33% reduction in runtime is a deal breaker for you; but honestly, when you have people willing to change primaries every 20 minutes with incandescent lamps like the Surefire P61 and P91, then getting 30 to 40 low-cost minutes between rechargeables in an LED light is probably acceptable to many.
As far as "horsepower" goes, rechargeables are always the winner over primaries. This is a known fact backed up by competent opinions and discharge graphs everywhere. The E2DL and L4 both run at full brightness on rechargeables for the quoted runtimes.
Now, to address your concern about the longevity and cost effectiveness of Li-Ions. I have been running my Surefire L4 on Pila 168 Li-Ions that I purchased over 4 years ago. I have two 168s that I rotate in succession, and they each have over 200 full discharge cycles on them; I don't recharge them until the L4 kicks out of regulation. I get about 40 minutes of runtime per charge on one Pila 168 versus 60 minutes on a set of 2 primaries. With my conservative estimate of 200 recharge cycles on each Pila, I have run the L4 for about 16000 minutes. That's 534 Surefire 123 primaries, which at $1.75 apiece is $935.00. I spent $95.00 on the Pila 168s and a Pila Charger. Some people here have said that Pilas are a more premium battery than the AW cells that are now so widely used, and as such, may hold up longer. However, these claims were comparing the AWs of a couple of years ago, and I don't know that the difference in quality still applies. Even if it does, you can get AW cells for ½ the cost of Pilas, which should more than make up for any shorter service life.
To answer your question about rechargeable compatibility with your E2DL; there are a lot of people on CPF saying don't use 3.7v RCR123s with it, but only one so far backing up that statement with an actual over-voltage occurrence. When I got my E2DL for Christmas, the first thing I tried was to run it on one of the Pila 168s, which is the equivalent voltage-wise of running on one 3.7v RCR123. It does work, and will have a long runtime, but is much dimmer than running on 2 primaries due to the E2DL having a different regulation circuit than some other Surefire lights like my older L4. So I then looked on CPF to see what other people were using. I didn't find much at all about using rechargeables in the E2DL, but there were 5 or 6 people saying they were using AW 3.7v RCR123s without issue; so I ordered some from Lighthound. My brother and I both received E2DLs for Christmas, so I have been using the 3.7v RCRs in both lights thru approximately 4 full discharge cycles without issue. However, about a month ago, a post popped up from username "The Sun" where he is saying he had a problem out of one of the several E2DLs he owns while using 3.7v RCRs. So he's 1 for 3 with problems, I'm 0 for 2, and the other posts are 0 for 5, giving us a a failure rate of 1 out of 10 lights. Possibly his experience was a fluke. I'm still using mine with the 3.7v 123s, but if another person posts an issue with them, I'll be switching to the 3.0v LiFePo4s or regulated 3.0v Li-Ions. There are some further capacity and quality trade-offs with those 2 options, however, and that's what kept me from going with either of them in the first place.
It would be much appreciated if anyone who has had an actual problem using 3.7v RCR123s in a Surefire E2DL would let us know about it.