I would accept the bitcoins.
You could get passed counterfeit dollars, or one of you could lose the dollars in transit. There's risks either way. And legally, you're supposed to report the net gambling winnings as income, not matter what form they come in.
If you're planning to immediately change the coins to dollars, you don't really have much risk of gaining/losing money because of price change - but if you hang onto the coins for a few days, you may see a real price difference. It's been on a tear lately - Bitcoin was around $900 on Christmas, rose to the high $1100's on January 5th, plummeted to $834 on rumors the Chinese government was going to ban it, and has been recovering because China put out a statement saying it's not banned, it just shouldn't be used as cash - they consider it a commodity and gains/losses should be reported as if it were any other commodity.
Whether it's bitcoin or dollars, you are technically liable to pay tax on the winnings as "income" in one way or another. If you took your payment in ounce of gold, it would be the same deal - for tax purposes, you can pretend it's gold and you'll be doing the right accounting.
If it were cash being transferred electronically, there's no less of a record than if you accepted bitcoins into an account at, say, Coinbase.
You can open an account at Coinbase, have the friend transfer coin into your your wallet at Coinbase, and you'll be certain the coins are good and that the friend can't reverse the transaction. Then you can sell the coins for dollars through Coinbase; they take a 1.5% fee if you put the dollars directly into a cash account with them or into a regular US bank account, or they take a 4% fee if you put the dollars into a PayPal account. The money going into any of those accounts would, of course, leave an electronic paper trail.
If the cash were being transferred hand to hand, of course, there'd be no record with your name on it (or theirs.) You can look to see whether there are Bitcoin ATMs anywhere near you. If so, you can open a bitcoin wallet anywhere, or establish your own with software. Then you have you friend transfer the bitcoin to you, and then you go to the bitcoin ATM to pull out the cash. This won't leave an electronic trail of any kind, other than the fact that it hits your bitcoin wallet - which doesn't have to be connected to your name in any way.
Basically, bitcoin behaves like electronic cash. Just like paper cash, it leave an electronic trail going into or out of your accounts.
Your friend may be offering you a bonus if you take the payment in bitcoin because he won't create an electronic paper trail showing that he made a profit on the coin. If he cashes his coin, he's supposed to pay income tax (if he mined them) or should pay capital gains (if he bought them cheaper and sold them higher.) Again, same accounting as if he were offering gold that he had mined himself, or that he had bought back when gold was only $600 an ounce. If he needs to sell coins to have the cash to pay you, but doesn't want to report the income, sending you the coin directly will cost him a lot less.
If you want to keep the bitcoins as bitcoins - and speculate on whether they'll go up or down in value - just leave them in your wallet. (But a personal wallet, not a wallet on a bitcoin exchange site. You don't want to worry about what happens if the site goes down next month or next year, so only move your coin to an exchange site when you're ready to exchange coins for dollars, or vice-versa.) Bitcoins have been very volatile of late, but seem to be on an upswing whenever there isn't a momentary panic for one reason or another. After the latest China scare, it has risen back to the $900 range where it was at Christmas... but back in October, it was closer in the low $600's range. While bitcoin is in your coin wallet, it's like a commodity that has the volatility of a high-volatility stock, because the environment keeps evolving... but if you convert it to cash in the same hour as you receive it, you're in no real risk.
https://coinmarketcap.com/currencies/bitcoin/#charts
Actually, if he already has the bitcoins, paying with them is ridiculously easy,
for him. That's not a reason to offer bonus. More likely, he's sitting on a capital gain on the coins and doesn't want to report it, and using the coin to settle a gambling debt allows him to do just that.
I think it comes with the same amount of baggage as US Dollars - but we're all very familiar with the baggage of US Dollars, and most of us are not familiar with the baggage of Bitcoins. For example, if my apartment building burns down, my bitcoins are fine... but I'll lose my poker roll, which is US Dollars!
