I don't really agree that a desktop burns more electricity than a laptop..
For instance, I'm sure my alienware laptop burns more electicity at full tilt than my little brothers dual core desktop at full tilt, it really depends on how you are running it and how hard you are working it..
When cooling is concerned, it is harder to cool a laptop, less efficient heat dissipation, so a laptop has to run its cooling fan harder than a desktop to achieve the same cooling..
It really depends on how hard you are running it too.. If you are talking about idle efficency or load efficency..
For instance, if you want your computer to consume less energy, running a light linux distribution will consume wayy less power than windows 10 when it's just sitting there idling.. System processes are much less intensive, so background power consumption is lower..
Run linux to suck less energy..
It's mostly about what you are going to run on your computer, the higher resolution your monitor is the more energy it will take to produce those graphics..
Watching a video @ 360p is going to take a ton less energy than watching the same video @ 4k resolution..
A bigger computer is more about how hard your computer CAN run at full tilt than what it runs at idle given the same operating system..
Long story short, if you want to consume little energy and don't need beastly processing performance, I'd recommend a HP stream and put linux on it..
I really don't know if a smaller processor will consume less energy at the same load as a bigger processor.. A bigger processor may very well be more efficient at the same load running 10% of its capability than a little processor running 90% on the same load..
I haven't really put much thought into processing efficiency, other than running full tilt such as Bitcoin mining..
I do know that if you run an older graphics card at full tilt mining BTC you will burn more $ in electricity than you make in Bitcoin, compared to the latest and greatest graphics cards, they will actually be profitable as in you make more in BTC than the electricity you consume costs, so at full tilt they are definitely more energy efficient than older ones..
I also do know that the new AMD A10s with integrated graphics are some of the most efficient running full tilt mining some crypto so maybe they are more efficient on other tasks too.. Other, smaller, and especially older processors can't even dream of achieving the same energy efficiency at that task..
They will burn more energy at full tilt than some others but as far as efficiency for actual computing power for the amount of electricity they use they are the best at that..
So newer is more efficient as a general rule..
Then with a laptop you have to think about charging a battery..
Their is no way on gods green earth that charging a battery and then using that energy is going to get you anywhere near the efficiency of just running off that power source directly..
I'm sure you RV gurus know a bit about battery efficiency, and the fact that you have to put say 1kwh into a battery to then later be able to get say .8kwh out of that battery..
No matter how efficient that battery is you are never going to get 100% out of it that you put in, just like your coach batteries..
If you are very concerned about energy efficiency at low/average load then their is much research to be done, but I bet the difference is quite negligible in reality..
Modern tech is more efficient than older, linux is more efficient than windows, batteries charging then discharging is not efficient ever..
Will it really make a practical difference?
If you want to compare an ancient laptop running windows off a battery charge to a modern core I3 or something running linux on direct power, then maybe yes..
My GFs HP stream goes forever on a charge and doesn't even have a cooling fan because it's not capable of eating enough electricity to make too much heat.. Like $225 brand new.. If you can find yourself a relatively beastly A10 and run it with no battery it may be more efficient, definately more efficient than something old like a Pentium 4..
Something to think about for you boondockers with solar..
If you regularly are getting more energy out of your solar than you need to keep charged up for your everyday energy needs, you could burn up that extra electricity mining Bitcoin and make some money off of that free electricity that you otherwise would be wasting, no matter how inefficient your computer is, if you are burning waste energy that's free money..