I'm specifically referring to applications (like Chrome) that you use interactively in the foreground. When using one of these applications, your device is not off or in sleep mode - it is on, you are interacting with it, and it is either consuming more CPU or less. A memory-hungry, CPU-light design drains your battery more slowly than one the other way around.
Additionally, the extra power cost of adding more RAM to a device is very low relative to even using 25% of total CPU TDP. [1] gives 3W per DIMM for DDR3 (which is an upper bound, given that LPDDR3 will consume far less power while fully on, let alone in deep sleep mode) and [2] gives 2.5W for DDR2.
Edit: aha, found a paper[3] on RAM power consumption in a phone. Far less than 5% in either "suspended" or "idle" states, under 10% in almost every other benchmark, and universally lower than CPU power consumption.
[1] http://www.buildcomputers.net/power-consumption-of-pc-compon...
[2] https://superuser.com/questions/40113/does-installing-larger...
[3] https://www.usenix.org/legacy/event/atc10/tech/full_papers/C...
One problem is that CPUs have various ways to use less power or even switch off parts when not in use, but you always pay the same for RAM.
For battery-operated devices that sleep most of the time such as smartphones, that means being careful with memory usage is the way to go. I think that’s part of the reason iPhones ship with less RAM then Android devices (reference counting needs less RAM than garbage collection for the same performance level)