fivemega bipin holder with TL-3 bulb and 2xAW R123 = a bit whiter & brighter than the LF bulb in my E2 (I have 3 setup - stock, LF, and TL-3)
The TL-3 bulb will draw about 1.3A off of those RCR's, the EO-E2R draws about 1.0A. You should have no problem running the EO-E2R continuously on good RCR123A cells while they may overheat at the TL-3's draw rate. The TL-3 output may be slightly more than the EO-E2R, but it won't last.
I had a Streamlight TL-3 and I recall the output was less and more yellow than my Sure-Fire C3 with a P90 or HO-9 lamp assembly. And the EO-E2R already puts out alot more light than the MN03. I would gauge it somewhere between an MN03 on fresh batteries and a P61 on fresh batteries, closer to the P61.
My TL-3's output was more yellow than any other incandescent I owned and this was on two 17500's. How it could be more white than your EO-E2R I cannot imagine.
I do not run my EO-E2R often, but I run a P90 on two RCR's (which draws about the same current as the EO-E2R) in a Brinkmann Maxfire several nights a week for extended periods and get reasonably good runtimes with it.