http://www.basstipoftheday.com/About-Round-Wound-Bass-Strings.htm About Flat Round Bass Strings :
When the wire wrapped around the plain wire at the core of the bass guitar string is a flat ribbon of steel or nickel, the string is referred to as a Flat-wound string. Flat-wound strings are a throwback to the days when all basses were of the stand-up variety. Flat-wounds give you the mellow. Round "thump" of a stand-up bass. They also prevent any string noise, as they will be 'friction-less' to the fingers of your left hand. flat-wound will last a good deal longer than round-wounds. The downside is that strings of this variety can sound "lifeless" when compared to their round-wound cousins.
About Half-Round Bass Strings :
There is another alternative to the flat-wound and the round-wound strings. These are called half-rounds, or ground-wounds. Again, the principle of the string is the same, a plain wire at the core surrounded by another wire wrapped around it. The difference lies in the fact that the wire that is wrapped around to core has been either ground down until the surface that your fingers meet is flat, or the wire was split down the middle before it was wrapped around the core, producing the same result. The advantage that these strings offer is the sound of the round-wounds (bright and crisp) with the benefits of the flat-wounds (reduced string noise and easier on the frets.)
About Round-Wound Bass Strings :
Round Wound Bass Strings. When the wire wrapped around the plain wire at the core of the bass guitar string is round, the string is referred to as a round-wound string. Round-wound strings are used today by most rock and blues players for their punchy, crisp attack of the string. One downside to round-wounds is that they will wear out your frets faster. There is also considerable "string noise" produced when your fingers run up and down the neck.