Patrick the ARB is slightly more efficient than the Dometic 50. Pat Anderson had a ARB, and I believe that his 100 watt solar panel was just not quite enough at Powell. You have different ambient conditions--both the time of year, and in the PNW climate. So there may be more draw in the summer.
We find that 30 amp hours is a good average for our dometics over a 24 hour period. We use one as a freezer and the other as a refrigerator. We use about 30 amps each 12 hours, and put that back into the group 31 AGM battery over 2 hours, using a 30 amp dedicated charger. (We use as an end point when the charger has dropped to 3 amps, and the charging voltage is getting to the mid 13 range--close to float stage, well out of bulk and absorption phases.
If you try and use the charger which comes with the boats, it is difficult to catch up. I have also been told that running those charges at max capacity shortens their life span. I have had a number of them give out on me. I solved that with a 20 amp 3 bank MasterVolt upgrade. I also highly recommend a dedicated meter to monitor amps used and battery voltage, like the Victron 600 or 700/702.
I am experimenting with a small volt/amp/cummulative amp meter I got off Amazon for about $19 which I will just use on the dedicated freezer/refer battery.
(Bayite 6.5 - 100 V DC, 0-100 Amp DC. (not water proof, and requires manual reset). But cheap--and has good feedback.
There are several other threads on these type of refers, the pitfalls, and issues keeping them charged.
http://www.c-brats.com/viewtopic.php?t=22018
http://www.c-brats.com/viewtopic.php?t=23082
As far as charing with the engine--it depends on the size of alternator, available amps, other draws, temp etc. We have a Honda 90, which only puts out 17 amps--and not all of that is available.
Greg, there are lots of variables with how long the ice will last--how often you open the cooler, if you take things out and put back in, the ambient temperature, If you keep a damp towel over the lid of the cooler, etc. We found out Coleman extreme to be good coolers, but Powell is not a great place to test for ice, since the ice is very granular, probably kept at just below 30 degrees, and a high ambient temp. We also have and "outer Banks" (similar to Yeti), and found it holds cold/ice better than the Coleman--by just a little, but it is a bigger chest, so we used it--but finally went to the two compressor driven units for a long time on the hot lake.