I thought about this and I decided that slants would be a better choice, but in practice I ended up using plates.
If you store a dish next to a slant for several months, you will notice that the dish eventually dries up. The slant remains hydrated for longer. Sometimes slants might also be more convenient to store or move around in a rack.
That said, as a small hobbyist I don't really need to store strains for so long, and I prefer to refresh them often. So I just grow multiple plates at a time, do some agar to grain transfer, and stack the remaining clean plates in the fridge. This works fine, but I do refresh at least every 3 - 6 months.
I am more paranoid about liquid cultures and I don't use them for long term storage. One excuse I can come up with is that if a contaminant reaches the liquid culture during long-term storage, it will mix throughout and it will contaminate the whole thing - whereas in the solid the contaminant might remain localized near the edges. I also have my crank theory about liquid cultures: I suspect that even if stored in the cold the mycelium will remain more active (and age faster) when suspended in a liquid than when resting on top of a solid medium. But this is pure speculation, I have not looked into the research, and maybe the mycelium rests just the same.