The answer is a clear
it depends.
Some classes are more expensive than others. I can buy two (top) 2WD buggies for the price of one (top) touring car. Of course there are cheaper TC options and when comparing those to Off-Road, maybe even 4WD buggies, you'll get a very different picture. Also pan cars / F1 are usually quite a bit cheaper than TCs. And that's just talking about buying
new cars. So, it really depends on what exactly you end up buying. Personally, On-Road has been quite a bit more expensive for me - but that is because of the choices I have made.
Luckily the electronics being used is the same for both On-Road and Off-Road, so no real difference there. Except that maybe, due to the nature off Off-Road for the jumping and bouncing, more vibrations, open wheels (more often than in On-Road since there's tons more buggies than F1s out there), chances of damaging a servo or ESC over time could be slightly higher. Still I'd say IMO
not significantly so.
That leaves all the "consumables".
Let's start with bodies. On buggies they usually last a
long time, up to several years. However, what buggies do easily destroy is their wings. Trucks are a different matter. Especially Short Course Trucks quickly and easily destroy bodies (and these are also the most expensive of all to replace), while Stadium Trucks are somewhere between buggies and SCTs.
While on the On-Road side... bodies usually don't last very long (except maybe for F1 bodies). Of course it all depends on your track as well. A tight little indoor track will cost more bodies than a wide open outdoor facility should. And to be fair, all cars with open wheels (like buggies and F1) may protect their bodies better... but at the cost of a more vulnerable suspension.
Lastly, tires. As has been said earlier in this thread, in On-Road you usually have spec tires in the rules of most classes so you don't have to buy or carry any options. These spec tires are usually also pre-mounted and glued, so rims and inserts are also nothing to worry about or fiddle with. However, all this comfort makes them quite expensive, since you cannot re-use any of it. Now, how long do they last? Again, it depends. Some tires last longer than others, but the most important factor is the surface you are racing on, and with how much power. On carpet, tires will usually become a little slower after several runs, but they are still usable for much longer, if you're not chasing lap times. On asphalt (even on wide open tracks with clean and very fine asphalt), you can literally destroy (some) tires within only a few runs, even in (super) stock classes. Of course tires will also wear faster in modified than in stock. That is of course valid on the Off-Road side of the hobby as well. But while there are pre-mounted combos available in Off-Road, too, it is much more common for people to choose rims, inserts and tires and glue their own wheels, which can cut costs significantly, since you can often reuse both rims and inserts after removing the tires again. Spec tire rules are less common than in On-Road, but at least in my area, even when there is no spec tire, choice of legal tires is usually limited to a few options for both carpet/astro and clay/dirt each, and out of these options, usually only one turns out to be popular and working on most tracks - again: this is in my area. In other placs in the worlds, you may really need to get different tires for each track, or even for different conditions on the same track, (be it weather or just time of the day that is changing) to stay competitive. Personally this would drive me nuts, but some people would hate not having 25 different clay tires to fiddle with... people are just different.
As you see, there's just too many variables to tell which is more expensive than the other in general.