In the system you have described, this is not accurate.
Batteries must match - same type, age, size, equal wiring, etc. when they are tied into a
full-time bank, but when they are only tied during charging, that is not a requirement.
The only thing that matters when charging, is that they both specify roughly the same charging voltages. And all 12v lead-acid batteries except gel type do specify roughly the same charging voltages.
In other words, the charging system will hold the "12v bus" at a certain voltage - on my truck it's 14.5v - and each battery will suck (well, suck for a few minutes, after that they basically just sip) however much juice it can at the moment depending on that battery's internal resistance, the wiring and the supply voltage of the bus.
Now I'll...um...examine...your example...
Pre-trip, you open the hood and flip the switch to tie the batteries. Post-trip you open the hood and flip the switch again to isolate the batteries from each other, and your second battery becomes just a backup to start the truck in case you draw down your primary battery too much.
Since the batteries are NOT tied while being drained, and only one is actually being drained, a mis-match doesn't matter. The second battery cannot be a "burden to the system" - it's not connected to the system (or as I would say, "the bus").
As you say, one battery will draw down quicker than the other. Well, yea...especially the way you're using yours - where only one is being drawn down anyway.
So you're not going to get equal longevity even if you have a matched set - the battery that is actually being used will wear out, while the other battery, which does nothing except get a top-off charge whenever the truck is running will last forever.
Also, from your original post:
Hrmm. Dunno if you're using the "royal we" here, but that's not the way I do it, and I think probably not the way most people do it.
The way it's commonly done, is to do it the way your Big Rig is done - one battery for engine starting/chassis use, and the second battery to run aux loads. Then most people either use a manual switch as you do, or an automatic isolator (commonly solenoid type rather than diode type) as I do, to tie the batteries when the engine is running to charge them.
I use a starting battery for chassis use, and a deep cycle for aux loads. (In other words - the right tool for the job.) They are not the same size, age, type, manufacturer, etc. - and it doesn't matter. They both want to be charged to 14v+ and the truck's charging system does hold the electrical bus at 14.5v when engine RPM is above idle.
Since they are separated when the engine is off, it doesn't matter that they don't match and the deep cycle will certainly wear out faster, because it's doing all the work of supplying the aux loads while the engine is shut down. The chassis battery does nothing while the truck is parked.
I've worn out and replaced 3 deep cycle aux batteries in the (uh...can't remember offhand...6 years or so) since the last time I replaced the starting battery. Next time I replace the aux battery, I'll probably do both since the chassis battery is about due to be replaced anyway.
(And yes, 3 deep cycle batteries in 6 years is a lot of batteries, but I'm semi-retired and use my camper a lot. I also consider the house battery in MY camper to be disposable and so I just beat the unholy crap out of them by draining all the way, not always recharging ASAP and not always recharging them fully when I finally do get around to charging them. Basically, what every expert tells you not to do - I do regularly. I don't make a hobby or a career out of babying, nursing and nannying batteries. So personally I just buy cheap deep cycle batteries and hammer them into the ground and replace them regularly.
But, also consider that those 3 batteries cost a total of...I dunno...maybe 250 bucks. About the same price as buying one good AGM deep cycle and taking care of it to make it last while damn near full-time living in the truck. And even if I did spend the money and take the time to baby a good battery - would it last for 6 years of almost full-time use? Unlikely.
And I ALWAYS DO spend the money to get a good quality chassis/starting battery, because I want the truck to always start, and I'm not going to abuse that battery anyway.)