Larger wire will have less resistance. However, the resistance of the radials in either case is negligible compared to the soil resistance, so I wouldn't worry about it.
Longevity would be my concern. Commercial broadcast towers use 10 gauge bare wire. Anecdotally, there are plenty of amateurs happily using 18 gauge wire.
Corrosion depends on many factors. Corrosion rates could be anywhere from 0.0002 to 0.15 mm/year, depending on soil conditions. Solid wire will last longer than stranded, due to decreased exposed surface area.
18 gauge wire has a radius of 0.51mm. Most soils won't be especially aggressive. At a rate of 0.0002 mm per year, it takes approximately 2500 years to corrode all the way through. So assuming favorable soil conditions, you'll be dead long before the wire rots away.
I think the bigger concern is mechanical strength. Digging animals can chew through wire or push it up. Frost heave and thermal expansion/contraction can cause the wire to pop up where it's subject to snags by foot traffic or mowers. Digging to plant a tree, etc. could cut a wire with a shovel. I'd expect to lose more radials this way than by corrosion. In my freezing, mole-infested location I bury the radials to anchor them more securely.
For the amateur, repairs are cheap and easy. So economically it makes little sense to spend a lot of money on robust wire. If 18 gauge wire hits the price point you need to install enough radials to have an efficient antenna, I'd say go for it.