The disadvantage of both these options is that you have to leave the crank battery connected to get the advantage of charging the crank battery when you plug in the house.
The first year I had my (used) RV, it never occurred to me to disconnect the chassis battery when in storage. The parasitic draw from the radio or something drained the battery and ruined it, which I discovered the next time I wanted to use the RV. I didn't make the connection at the time -- I just thought the battery was probably due. So, after replacing that battery, my PC gave me a clearer lesson -- the computer or switch or whatever controls the courtesy lights under the doors chose the moment I put it back into storage to fail "on", which destroyed my new battery. I discovered this a week later, when I tried to take the RV to get it inspected.
At that point, it finally dawned on me that leaving the battery connected in a vehicle that isn't driven for months at a time might be a bad idea. So after another $150 for another new battery, I invested $10 in a battery cutoff switch, and another $40 for a trickle charger. I now check on my RV more often and I rotate the trickle charger between the RV and the Smart Car toad, which also has a battery cutoff switch. And, to make sure the courtesy lights can't get stuck on again and leave me stranded in Timbuktu some day, I unscrewed the courtesy light bulbs, for good measure.
By the way, the other thing I learned in that first year was that it's a very bad idea to leave the house plugged in all the time while in storage. That dumb Parallax converter the PC came with cooked $300 worth of house batteries. After replacing the house batteries with AGM's, I replaced the Parallax with a smart converter (Progressive Dynamics PD9245CV Inteli-Power 9200). But I still don't leave it plugged in all the time.