Well, a number of us have done both
I have four batteries and four solar panels. The batteries happen to be lithium's, but that's a different subject. Indeed people do go well beyond 4 batteries. In my case, that is all that would fit in "dead space" on the trailer. If I had more room, I'd put in more batteries.
Weight wise, lithium's do help a bit ( = they are lighter). On a "large" trailer, even 4 or 6 lead acid's aren't likely to overload your axles. Depending on where they go, they could have an impact on weight distribution in the trailer.
The advantage of solar is that it's quiet and it's "free". The disadvantage is that it pretty much dies when the sun goes down (no matter how many panels you have). Batteries are always there, but they have only so much capacity.
The "holy grail" for many people is running the A/C off grid. Doing that for an extended length of time ( = hours of run time) is going to be exciting without a generator involved. If that is not part of the deal then one can come up with a practical battery / solar combo that will work off-grid at least as long as your water tanks hold out.
Some math (based on a lot of guesses) :
1) RV pulls 50AH a day ( 24 AH for fridge and 24 AH for everything else)
2) In 10 days you have run through 500AH
3) With lead acid's run to 50% that's 1000AH of battery
4) At ~ 100AH per battery you have 10 batteries
1) Same 50AH per day
2) 400W ( = 4 panels ) on the roof
3) Typical day in a shady location provides 500 to 1,000 WH ( = 38 to 76 AH)
4) 200 AH usable batteries (so 4 lead acid's)
5) You can easily run for 10 days and likely much longer
If you buy fancy batteries at the prices some people seem to pay, ten AGM batteries will cost you quite a bit. In some cases lithium's actually would be cheaper than what some people spend. If you go with something like Trojan T-105's (which *are* good batteries) you should not be paying "near lithium" sort of prices.
One side benefit of solar is that it can / may be used to keep the batteries charged when in storage. That assumes you store outdoors and are ok with leaving the solar running. I see no problem with the "leave it running" part. Storing outdoors is not the way we do it.
Lots of options, lots of choices. As with just about everything in life, you decide what you can afford to do and go with that.