The battery life argument is an interesting one, I've always been on the side of "It doesn't matter in Theory, they will both use the same amount of energy. You can't get free heat on your coil, if your coil is putting out more power, it's using more power. Ohms, Ams, Watts, etc are all relative and dependent upon each other, so simply having less theoretical amp draw doesn't really matter.
But I took the OP's question as more related to the quality of the vape, not the life of the battery. Here is my theory on it:
LR stuff will obviously put out more heat, flavor, vapor, etc at the same voltage compared to higher rez stuff. How do they accomplish the lower resistance? From all the attys and cartos I've torn apart, it appears LR stuff has less coils. Higher rez stuff has more coils (and thicker ones in my experience, although thicker wire would lower resistance, a longer coil brings it high enough to overcome that evidently.
The LR coil will get hotter at a given voltage, but the higher rez coil will have more hot surface area to vaporize juice.
So, which gives you better performance? Less surface area, but at a higher temperature, or more surface area, at a lower temperature? Obviously from experience we know that LR will outperform SR with the same voltage, but what happens when you raise the voltage?
When you start cranking the voltage up on LR stuff, that smaller, thinner coil will get hotter and hotter. Too hot eventually. You'll burn your wick or filler, your juice, or pop the coil.
When you start cranking up the voltage on SR or HR stuff, there is a lot more surface area to vaporize juice from. At the SAME voltage obvious that surface area will be cooler, thus giving us less vapor. But as voltage goes up, you have more surface area to distribute that heat.
So think about this. A 3ohm coil (no wick, juice, or anything, just a coil) with twice the wraps of a 1.5 and thicker wire compared to the 1.5 ohm coil. Fire them both up side by side with the same voltage, and use an laser thermometer to read the temperature of the coils. The LR will be at a higher temperature, but the HR will have a greater VOLUME of heat.
Now, forget wattage and voltage, and just think about coil heat. Take that 3ohm coil with way more surface area compared to a LR coil. Get that coil to the same temperature as the LR coil was at lower voltage.
Figure out where I'm going with this yet? Equal wattage does NOT mean equal heat at the coil. It never has, never will, and that's what confuses the heck out of people.
Imagine the difference between a pocket torch lighter, and a bonfire. The pocket torch lighter will reach temps of thousands of degrees. The Bonfire won't reach temperature anywhere near that. So, using current vaping logic, the pocket torch lighter will burn a three foot long, 2 foot diameter log better than the bonfire. We know that's not true. A huge bonfire will consume the log in no time, it would take you a week to burn the log down with a pocket torch.
See the comparison? It's not only temperature, but volume of heat we are looking for. I don't know if volume of heat is a technical term (probably not) but hopefully my bonfire reference will explain exactly what I mean.
If you want more vapor and more nicotine, LR isn't the answer, because LR will just increase the temperature of the coil. The only time LR will give you more vapor is if the coil is not already at it's optimal temperature, like using high rez at low voltage.
Ideally, it would work like this: Adjust heat of the coil up and down to find the sweet spot were FLAVOR is exactly where you want it. Some juices produce slightly different flavor at different temps (I notice Pluid really opens up at higher temps) so find whatever you prefer.
To adjust how much vapor you get, either use more or less wraps on the coils. More coils equals more vapor, because of the increase in surface area. More juice can be vaporized at the same time. Adding more heat will only increase vapor up to a point, the point where the PG/VG vaporizes. Any more heat and you are just burning juice with no increase in vapor.
A coil with more wraps/thicker wire will also not cool down as much as a smaller coil when the air passes over it while you are inhaling, which means more consistent heat at the coil, compared to a smaller coil that will cool down faster when air passes over it, and be more dependent upon what type of draw you take. Faster draw will cool the coil down more, this is true of any coil, but more wraps and/or thicker wire means it's less effected.
So, all along, we have been using ONE factor, Wattage, to adjust BOTH flavor and vapor production. When we should be going more coils at the same temp for more vapor, and more/less temp for adjusting flavor.
So, to summarize, to increase vapor you need to increase the number of wraps on the coil. To adjust flavor you need to adjust the heat of the coil. If you have a 7-wrap coil at the SAME temperature as a 3-wrap coil, the 7-wrap will put out way more vapor, as there is roughly twice the surface area, at the same temperature.
The confusion comes in because people think the same wattage means their coil will get just as hot, which is wrong. A 1.5ohm coil at 7 watts will not be the same temperature as a 3 ohm coil at 7 watts, even though vaping logic says if it's the same wattage the heat is the same. In theory yes, in the real world, no.
Why? because we are bringing tons more factors into the chain than JUST the electrical circuit. Right now we mainly use electrical laws to describe our vape, but we also have factors that are in the realm of Physics, Fluid Dynamics, Materials science, etc. You would, quite literally, need to be a jack of ALL trades to completely control the vaping experience.
My advice, if you want more vapor, go with something in the 3ohm range, then crank the voltage up until flavor suffers. That will give you more vapor volume and density than using something 1.5 which has been cranked until flavor suffers.
LR, SR, HR, etc should not effect flavor. Temperature at the coil effects flavor. You will get MORE flavor with more vapor, but the flavor will remain unchanged. Just remember, at the same coil temp, the more wraps you have, the more surface area, meaning more vapor. If you have one pot of water on the stove boiling, adding more heat will slightly increase the boil, but adding another pot of water at the SAME temp will greatly increase the amount of water you can turn into steam. More wraps is adding another pot, but the temp has to be the same.
EDIT:
Keep in mind while reading, I'm assuming the ability to adjust voltage on behalf of the user. If you have a fixed voltage device, like a 3.7, LR will most always mean more vapor and heat. Because at 3.7 a high rez coil won't reach optimum temp, so you are playing catch up the whole time.
