well, there are basically 2questions, and i have 2 answers. as mentioned, 1k@4ohms and 1k@1ohm in an amp is set up differently. really, current is something that is allowed to pass, determined by how much resistance is present between a voltage source. (both in static/meansured, and dynamic, i'e electromagnetic, thermal, and conductor ampacity limitations.) i mention this, because it is all too often over-looked, and amperage is mistaken as, and even referred as an applied source/effect, rather than a resulting effect.
so, let's look at the 2 different output sections. first, is the 1k@1ohm. it would usually be set at 35-45volts available on a good solid amp to give you the ~32vac needed. the 4ohm, would need to put out ~64vac, and could see 80v on a solid amp. the same exact power supply section could be used for either, but the control circuit would just monitor the output rail voltage to sustain the appropriate voltage at any power use level, up to full duty cycle, or gain (depends on type of power supply used)
there are a few different factors that effect efficiency, but the biggest is in the transformer, which is usually a "torroid" (circle thinggy with wire wrapped around it.) it should, but not always, match power transfer ability at it's most efficient level at/near full power supply duty. at power levels below that, the efficiency drops, since the driving magnetic field is lower, and less of it is transferred into the core. (more amps passed, equals more e.m. field) in a 1k, it is relatively typical to see 2-5a of current being used at absolutely 0 efficiency, during idle (on, no output) you can also see efficiency in the 40-60% range between 1/4 and 2/3 power. also, there is a bit different scaling on an unregulated power supply, and consequently often quite less efficiency.
back to the 2 amps. there are different ways they are set up. what i like to see in a 1k@1 amp is that the 2ohm output is half. this tells me that it was made to run easy, and efficient at 1 ohm when you see power levels more than half at doubble resistance, it indicates that the amp is being driven beyond what the power supply runs at full cycle. this is not always a bad indicator, as the amp could be built with components that can handle more current than what full cycle passes. if it is severe, you may get "bubbly" power, rather than solid, clean power.
1k@4: if the amp is made to run most efficient at 4ohms, then the efficiency at, say 2 ohms, would be more effected by heat and ampacity of the components in the amp than at 4 ohms.
that's my bits for now. in short, it depends a great deal on the transfer efficiency of the transformer between the power supply and output section at different power levels.