Silver isn't always silver. Financially speaking, it will all depend upon the price of silver when you sell. As the spot price of silver rises, the premiums on ASEs fall, so therefore the ASE will retain more premium over spot at lower prices. At higher spot prices that premium becomes less and less.
To summarize, you should lose less with the ASE's if the price of silver doesn't rise or falls even further when you sell. Conversely your profit margin should be higher with the silver rounds (or any silver bullion) if the price spikes again. All of this assumes you don't overpay or get a bargain on either. If the bullion has too big of a premium attached when you're about to buy, it makes the ASE much more attractive and vice-versa.
For the record, I really don't like the price of either of these items. Surely there are better deals out there. Unless of course, you're only buying a few ounces...then it really doesn't matter, or at least as much.