On a humbucker, there are two insulated-wire coils (one on each bobbin). Each end of the coils are routed to wire leads (for a total of four wires) that can then be placed wherever they are needed on a switch to achieve different wiring combinations.
With "coil splitting" a humbucker, you are simply taking one of the two coils completely out of the circuit using a switch. When this is done, the "hum-cancelling" feature of the humbucking pickup are nullified, as you're basically turning the humbucker into a single-coil pickup.
With the "coil-tap", you are in-effect adding another lead to each coil that "taps" into the coil at some point. With this method, you don't lose the hum-cancelling effect, but you also don't achieve a true single-coil pickup as there are still two coils in-operation.
The goal of each method (coil-tapping and splitting) is to reduce the resistance of the pickup (by removing winds from the coil), which typically results in a brighter tonality that approximates the sound of a strat or tele single-coil pickup.
As far as which is "better", neither method with a humbucker results in a sound that is exactly like a strat or tele pickup because there are other structural differences between those pickups and humbuckers. The magnet placement is different, the actual position of the pickup on the guitar is different, and the scale-length of the guitar may or may not be different from a strat or tele as well. If you want to keep the hum-cancelling feature, then the "tap" may be the way to go. If you want to more closely approximate the structural nature of tele/strat single coils, then the "coil split" might be the thing.