The only advantage of going for a progressive over a single stage is just speed. Some progressives can load over 1000 rounds per hour (mostly pistol rounds).
But, it comes with a few inconvenients, the increased number of moving parts makes the machine more tricky to operate and needs more care and maintenance. Accuracy would be slightly inferior to rounds loaded on a single-stage, since moving parts each require some 'tolerance' in order to move freely. Also, volumetric powder measures commonly found on progressives presses are accurate enough for safe reloading practices but it cannot beat the accuracy of weighted loads.
Fully progressives presses such as Hornady LN'L AP, or Dillon 650 or 1050 give the highest production rate of good quality ammunition.
Single stage presses such as Rockchuchers and similar will give the best acuracy, especially when coupled with premium dies, but this will result in a low production rate of premium ammunition. Also, SS presses do not require any 'conversion kits', let alone dies and a shellholder for a new caliber.
Bottom line, if you plan to reload many different calibers and do not shoot alot, a Single Stage would be the best bet. Progressive loaders are only worth if you shoot alot of each caliber. (I for myself have a Dillon 650, and reload 45ACP and 40S&W with it, and I shoot around a thousand of each per month, all my other 'low-volume reloading' (.44Mag, .308, .223) is done with a single stage.
A good compromise, would be the Dillon 550B press, it is not fully progressive, it is somewhat cheap to buy (compared to other Dillons), conversion kits are cheap, and there is fewer moving parts. Plus it's good for both rifle and pistol.