Firs thing to consider, is how physically fit are you?
A ten frame deep filled with honey can weigh 90 pounds. A ten frame medium 60 ish pounds. if your going to have twenty hives using 8 frame mediums might be the best way to save your back.
Beyond the weight issue, there is also the ability to exchange Frames anywhere you want, if you use all the same sized frames for brood and honey supers.. This is what i do. I use all ten frame mediums.. three mediums for the brood chamber = 5/8 of an inch or so taller than two deeps. I can steel last years honey super to start a new hive with drawn comb. I can swap in frames of capped honey int he fall if they have not managed to store enough for winter. i can move eggs up or down or over, anywhere I need them etc...
You can do that with ten frame deeps, using those deeps as honey supers as well, but as stated.. MAN they are heavy!
I have talked with a LOT of new beeks, giving classes and talks. MANY MANY of them start beekeeping using the two deep brood boxes with two medium honey supers. They do this because they THINK its how they are supposed to start, and that its the best way.. In fact, this is how I started. It did not take me long to realize the advantages of all mediums, and I run all mediums now.. i have a few deeps, it seems I cannot EVER get rid of them all.. inheriting deeps, either from a beek getting out of beekeeping, or when i buy out another beekeeper... But each spring as I rotate boxes those deeps are pulled and fresh mediums used to replace them.
it makes NO DIFFERENCE if you use deeps, or mediums. the bees dont care.
I have read often about how much MORE it costs to use mediums because you need extra equipment.. this is true. i figured it out, and found that it usually costs about seven dollars more for the extra deep. The wood is less expensive and saves you money, but you need an extra ten frames. If seven dollars is enough to put you off using mediums then beekeeping may not be the best choice of a hobby!
As i get older. I may begin to switch to 8 frame mediums. At the current time I am doing well with the 10 frame mediums. the choice of what to use IS dictated by YOU, and what you feel would work the best with your method of keeping bees.