There are a couple of issues to consider.
Counterfeiting: There are stiffer penalties for counterfeiting Government legal tender than there are for copying a generic round. The hope is that by buying a Government coin, you have a greater degree of protection. I think the FBI gets involved if anyone tries to fake an ASE, they don't bother for a generic round.
Cost: Government bullion coins can be more expensive than generic bullion rounds in most cases. You are paying extra for the brand, they are probably more recognisable, so easier to sell and you should probably be able to get the premium back when you sell, if you sell to a fellow collector/stacker. If you sell back to a dealer they may give you extra for a Government issued coin, but they might just buy bullion back for spot. It is worth asking your local coin shop/bullion dealer. Generic rounds are most likely to sell for less unless someone wants to add them to their collection.
Legal Tender Status: I actually consider this to be a drawback, a $1 face value on $20 worth of silver that costs you $25. What is the point? You are never going to spend it for $1, even if the SHTF. The only benefit I can see is with the government who might claim that, as it is legal tender, it belongs to them. But they will gladly deposit $1 into a bank account to compensate for the $1 coin they have taken away from you. I know there are concerns in America about precious metals confiscation. I can't see it happenning but really, what is the point?
Storage: Poured bars are cheaper than minted bars, rounds and coins. They fit into a safe easier, they don't need to be kept in capsules or tubes, you can get finger prints on them or you can get them scratched without affecting the value of them. But if the spot price drops so does the value of your bar. The only way the value will go up is if spot goes up, and this should raise the value of most bullion products by the same amount. There is unlikley to be much of an increase in their premium unless they happen to be a well known brand, limited edition or collectable in some way, it still surprises me the amount of money people will pay for a bar.
Coins need to be stored with a bit of care to make sure that you keep the premiums up, capsules, tubes etc. Milk spots, scratches, ugly patina, signs of cleaning etc. will all reduce the value.
So in summary, the choice isn't just in Rounds vs Coins
You have
Government issued proof coins
Government issued bullion coins
Generic proof rounds
Generic bullion rounds
Collectable minted bars
Collectable poured bars
Premium minted bars
Premium poured bars
Generic minted bars
generic poured bars
Local junk silver
World junk silver
Scrap silver
But not neccessarily in that order for everyone. I think I have a bit of most of those things.
You could buy one of those Kennedy Half Dollars, they seem to be a bit of a bargain!
