For no-compromise optical quality, go for the 70-300. Generally, dedicated telephoto lenses offer better image quality than the "do it all" type lenses, such as the 28-300. However, if you don't want to be changing lenses too often, the 28-300 would be a good choice.
As Janern mentioned, the 28-300 offers an equivalent focal length of 42mm on your D3100, which if you're using it for general purpose photos and telephoto shots you should be fine with. However, if you also want the ability to do landscapes, consider a Nikon 18-200 or the tiny Tamron 18-270. However, bear in mind that a new Nikon 18-300 is rumored for next January. Which these lenses would be great for the time being, if you're looking into upgrading to a full frame body anytime soon, they won't work as they're designed for crop-frame cameras like your D3100. For a full frame camera, you'd need something like the 70-300 or 28-300.
I personally use a 16-85 and I love it, for 95% of my shots it covers all the distance that I need, it's sharp, and the extra 2mm over the other DX zooms really does make a big difference. If I had the money right now, I'd probably pick up a 70-300 to compliment it.
Gear: 7 Nikon Nikkor AI-S and AF-S lenses, SB-700 flash, Nikon D7000, Nikon FM, variety of accessories
"There are no rules for good photographs, there are only good photographs."
- Ansel Adams