the standard battery is an IC (or IRC) which stands for a lithium
Ion
Cobalt battery. so the tenergy and the AW you speak of are the same "type" of battery, share the same chemistry make-up, but the AW is a protected cell. neither of these
batteries are really the mAh rating that they are listed as. AW has a reputation for having more accurate ratings, as well as better quality and consistency in sizing, performance, protection circuitry, etc. if they were true ratings, however, it wouldn't matter much because several things are in play here. the fact that you will use these in an e-cig (mod) configuration with an atomizer that puts a certain load on on the battery voltage and increases the amperage drain on the battery, means that all the numbers on the sticker go out the window, and the numbers that matter more are the discharge "C" rating/ amperage rating and the amp draw from the atomizer you are using. the drain on the battery increases with lower resistance atomizers, so standard 306s draw more amps than 510s which draw more than 901 and 801s, etc. of course low res attys will draw the most, the lower in ohm rating they are. so whereas there may be an amp draw under 2A with one atomizer type, using a Joye 510, 306, or low res atty can approach amp draws higher than 2A. this is a stress on the battery and greatly impacts the runtime, irrespective of whatever numbers were on the sticker to begin with. in the smaller size cells, all of this is very important because really only a few batteries will be able to successfully handle the amp drain from any atomizer. going with an AW IMR16340 or AWIMR14500 will put less strain on the batteries with any atomizer than would be the case with a standard ICR cell in the same size. "constant vape" is probably due to the cell's ability to supply the discharge rates and sustain the amperage draw routinely from the atomizer, no voltage sag.
battery energy density and capacity is a function of size and chemistry. ICR chemistry holds more than IMR and IFR (LiFePO4) in the same size. however, a 16340 and 14500 sized battery, no matter the chemistry makeup, is only able to have but so much energy density packed into it. so the differences at these small sizes tend to side with the IMR because you get the cell that is built to handle the amperage drain, and won't lose out on runtimes because the other same sized cell in the other chemistry is not able to hold substantially more to begin with. in bigger sizes such as 17670, 18500, 18650, 26500, etc. you have a wider range of ICR batteries that can routinely handle the amp draw of any atomizer and benefit from the increased runtimes over IMR and IFR chemistry cells. in those sizes, going with the IC or ICR battery makes sense from a runtime and performance perspective, but you may or may not feel more comfortable with the safety of an IMR at those sizes as well.
so more directly to your question, i think the AW IMR is the best bet at 14500, and that 600 mAh runtime will do better than the 750 or 900 mAh runtime with any atty. if you do notice a difference in favor of one battery or another that has a higher number printed on the sticker, or even see a graph comparing one to another under a given load, none of this will address the long term viability and efficiency of the cell in my opinion. i believe the IMR at smaller sizes like the 14500 will be able to sustain the performance over time, recharge after recharge, whereas the stress being routinely placed on the other same size different chemistry cells will shorten their life and decrease their performance. hope this helps a bit.