What I have learned about replacing 12VDC relays with power mosfets.
I first approached this idea about 11 years ago. I do not remember what the N channel that had a low rds at that time,(may have been IRFZ40, rds of 28milliohms) but I knew that no matter what the rds was that there would be a voltage drop and power dissipation because of the rds. I did some test on a Potter and Brumfield 12V relay that not only had a dc coil but the contacts were rated at 28VDC and 25A. I also knew that the power dissipated by the relay was two parts. 1. The contact resistance and the coil power. I also knew if the relay would remain energized at 1/2 the nominal coil voltage the power dissipated by the coil would then be 1/4 the power at full voltage.
The results of the test on just the contacts were: With the coil voltage of 12V and a 25A load the voltage drop across the contacts was 86.7mV(or 3.46 milliohms) With a coil voltage of 6V and the same 25A load the voltage drop across the contacts was 88.6mV(3.54 milliohms)
I wanted to test the contact resistance at half the coil voltage as I knew that the pressure on the contact could be related the strength of the magnetic field of the coil.
With these facts in mind I designed a built a relay coil drive circuit that energized the coil at nominal full voltage and then a short time later reduced the coil voltage to 1/2 the nominal voltage. The results at that time were that the total relay power(contact dissipation + coil power) was less than the current mosfet rds power dissipation. I also went ahead a designed a low voltage cutoff if the battery became discharged. At this time I was using batteries charged by solar panels and the relay circuit operated some 12V equipment.
If a IRFZ40 was used at that time the power dissipated at 25A would be 25 X 25 X .028, or 17.5 watts.
With the 12V relay with a coil resistance of 110 ohms, and the coil at 1/2 normal the voltage the power would be: 0.327 Watts + (25A x 25A x 3.54millohms)=2.54W, way less than the power mosfet. Even if the relay was at full voltage the power of 3.8 watts was still less than the mosfet.
I recently did some more research for the same thing. I looked for P channel mosfets as the drive for high side switches is easy. I found IRF4905 with a rds of 20 milliohms. Doing the math again with a 25A load we have 25A x 25A x .02 ohms or 12.5 watts.
A N channel mosfet IRF1404, rds of 4 millohms seems like the one to use as the power dissipated would be 25A x 25A x .004 ohms or 2.5 watts. For a high side DC switch then I would need about 12V +10V(gate drive) or 22 volts. My solution is to use a LT1054cp voltage pump to double the input voltage to drive the gate.
I don't know what the nominal contact resistance of the small auto relays is, but with a coil resistance of 85 ohms the power for the coil is 1.7 watts, as pointed out by MikeMl
At this point to me using the relay is still more convenient, and as Nigel said that relays are reliable.
I am still using solar panels to charge batteries and I am finding more ways to use the stored power at night. I plan to use more for some patio lighting with a timer and a control relay.