I'll answer your question, not caring if you have St. Augustine or Bermuda grass. I bought my place in 08, and it came with an asphalt driveway, about 180'. I know the guy I bought the place from, and he went with asphalt because it was cheaper. I don't think he picked a good contractor, though. The land is the side of a hill, and water has been getting under the drive and allowed cracking and alligatoring. My wife and I sealed the drive a couple times, to the tune of $500 each time, doing the work and buying the 'best' stuff at Menards.
The last time we did it, it didn't last a year. Got my money back, and had a local asphalt company spray coat it, twice in about 4 or 5 years. We finally had a company come in and 'oil & chip' it, so it looks like a gravel drive. We like the look, as we're in the country. BUT, it does track in, and you can't roll a floor jack on it, but that's what my 24x40 pole building is for. We've had complitments on it, and one neighbor asked about it for his new house.
Being that it's sloped, asphalt is good in the winter. The snow DOES melt the snow/ice quickly, but now that it's graveled, I can't use the snow blower, and I had to raise the blade up on the tractor. The snow still melts quickly.
So...it all boils down to the prep work. If my PO had spent the money to have it done correctly, this drive would still be in good condition, but he didn't. He probably went the cheapest route. I liked the look of asphalt better than concrete, but that's me, and asphalt in my case was more work. I've also heard people say that asphalt is cheaper on property taxes, as it's considered temporary. Don't know about that, though.