The main rationale for buying bars over coins is the lower markup.
In my opinion, that's insufficient reason to buy bars.
First of all, we're just talking a few percent. There is very little savings to be realized in buying bars over coins. And yes, I realize that we're talking real money here, whether it's a 2-3% markup difference on $1200 or 12,000,000, it's real money to the investor. BUT... why are you buying this in the first place? Not to accumulate the maximum number of ounces you can. That is irrelevant. You're buying gold to allocate a portion of your financial portfolio to the commodity. A dollar is a dollar. You might buy 100 ounces of gold bars, and I might only be able to buy 98 ounces of American Eagle gold coins for the same money. Or 97. Whatever. So what? Why are we doing this? If it's never going to be sold, it makes no difference what I have. It could be 100 oz. of Saran Wrap. No matter if it just sits somewhere until the Sun swallows up the Earth. What matters is what happens when we sell. And guess what? The same relationship exists with gold bars as gold coins: it costs more to buy than you get if you sell, and the coins are worth more per ounce than the bars. I can sell 10 1 oz. American Eagle coins for more than you can sell your 10 oz. gold bar. I just checked one site and based on their posted buy-sell prices right now, here is the comparison for a 10 oz. Credit Suisse gold bar and 10 American Eagle coins:
Coins: Buy: $12,506.50, Sell $12,156.50, Difference: 2.879% premium
Bar: Buy: $12,236.50, Sell: $11,806.50, Difference: 3.642% premium
Spot: Bid: $1200.80, Ask: $1200.50, Difference: 0.025% premium
I quoted the spot prices just for a frame of reference. My hypothesis here is it makes no difference what the spot price is. You're not buying nor selling based on spot. You are buying an object, a thing, be it a coin or a bar, and you will hold it for some period of time, and then sell it. It will still be the same object when you sell it, assuming you don't plan to melt the coin down, which would make no sense (nor would it make sense to melt the bar and obliterate all of its identifying information).
Regardless of whether you buy coins or bars, once you've made the purchase, the value of your investment will be determined by what you can sell it for, not what you paid for it, and certainly not (directly) what the spot price is. You will get less per ounce for your bar than I will get for my coin. And if you make this an apples-to-apples comparison, you will have slightly fewer ounces of gold if you invest the same money in gold coins, but you will actually be able to sell the coins for slightly more than the bars!
That alone should prove the fallacy of buying bars over coins.
But wait, Don Pardo, that's not all! Tell them what else they've won!
Liquidity. That's what you've won. In today's world, you could argue that bars are as liquid as coins. Not true, but not that far off. You will never have a problem selling an American Eagle one ounce coin, whether you're selling one or 10 or 100. Well, the higher the number, you might start to have problems. You can't just walk into a lot of gold dealers today with a suitcase full of 1,000 Eagles and expect to walk out the door with $1.2 million in cash. Some, I suppose. But others have pointed out that you will encounter some dealers who will balk at buying a gold bar. It's not as easy to verify as the ubiquitous American Eagle. And try selling a gold bar to one of your friends who is interested in buying a little gold. A 10-ounce bar is over $12,000. Chump change for some; life savings for others. But even if you have a 1 oz. bar, you will find some people who will be willing to buy your American Eagle coin who will be too reticent to fork over $1200 for a bar that CLAIMS to be pure gold. If they're never seen one before, they're likely to be skeptical.
The real question, though, is what happens when we're NOT in "today's world." What happens if TSHTF, or as my wife and I like to refer to it: TEOTWAWKI (mainly because it's fun to pronounce! "tay oh twak ee"). (Legend: "The shit hits the fan" and "The end of the world as we know it.") Most Americans don't tend to think this way because we haven't had any serious force of foreign troops fighting us on the mainland in 200 years, so we think of our society as permanent. But regardless of the probability you assign to it, there is a chance the shit really will hit the fan some day, whether it's from within or without. History suggests no society will last forever. So you have a breakdown in society, the banks are trashed, people are burning dollar bills to stay warm, neighbors are shooting neighbors who are trying to loot their pantries, and you're smug that you had the foresight to put 25% of your wealth into gold bars. Who is in a better position to buy stuff you need: You with your 10 oz. gold bar that the average Joe you're trying to buy from has never seen, doesn't trust, can't afford (how much toilet paper are you actually trying to buy?!?!?!?) and doesn't think he'd ever be able to sell/barter if he accepted it in trade? Or me, with my tubes of 1 oz. American Eagles? (and some fractional Eagles as well) The answer is obvious, and that's the other side of the liquidity "coin." My Eagles will be MUCH more liquid than your bars after TEOTWAWKI.
So, for me, these two reasons answer the question: "Any downside to bars?"
Answer: Yes. The coins will always be more liquid than the bars, maybe just a tiny bit more liquid if tomorrow is just like today and you can sell them back to the dealer you bought them from or another large, reputable dealer. But if that dealer is dead, his bricks-and-mortar store broken into, looted, and permanently gone, you want your gold to be every bit as usable as money. The American Eagle coins will always win that contest. And as I proved at the beginning of this post, they are every bit as economical (even slightly more so, although that wouldn't matter if it were a couple percent the other way) as buying bars.