Hi there!
Can anyone make a statement if OpenWrt based devices use more power than stock firmware? OpenWrt is known to have significantly more features. What are the differences?
(Background: my electricity bill is much too high and I run also a Raspberry zoo)
I cannot tell you how much of a difference OpenWrt will make vs the stock firmware with respect to power consumption (for several reasons, including how you have things configured and what, if any, additional packages you are using which could impact the processor utilization). However, it should not have a material impact on your electric bill.
Let's put this into perspective and do some rough calculations:
If this adapter is the same as you're using on your R7800, it is rated for 12V @ 3.5A (42W). Just to give some numbers, if the router is running at full capacity (unlikely) for the entire month, you'd be talking about 30kWh.
Let's assume your electric costs are ~$0.35/kWh (that is the "tier 2" for my area in Northern California), the maximum contribution of your router would be in the range of about $10 to your electric bill. Now, if we assume that the stock firmware only draws half the power, the difference would be $5/month. I think these are likely overestimates... you're probably only paying ~$5/month to operate that router, even on OpenWrt.
If you really want to test this, you can buy a device to monitor your power consumption and you could compare OpenWrt vs stock firmware. The power consumption will likely be related to the network bandwidth consumed at any given time -- so a speed test would be a good way to test the typical power consumption during high bandwidth periods.
All that said, the $5-$10/month to run this device is not necessarily a big number, but all of the little devices you have connected to your power will add up.... if you have a bunch of Pis doing intensive things like mining or other heavy processor load applications, you may be looking at around $3-4 for each Pi (the Pi4 has a 15W power supply).
The things that have a much more significant impact on your electric bill are likely to be your major appliances -- HVAC (even if gas for the heat, the fan can use around 300W+), refrigerator/freezer, clothes dryer, hot water heater (if electric), oven/stove (if electric), and even your lighting (especially if you're not using LEDs). But while the individual small things don't make much of a difference, the combination of them does add up, too.