Multi-cone speakers can work very well- many systems use a "2 and a half way" design, where the main mid/bass driver is complemented by additional bass drivers, usually in a separate enclosure within the cabinet. These extra drivers don't do mids, but just help out at low frequencies. The results can be very good (i.e the RX8s...), but the design is more complex, requiring more crossover components and, if poorly executed, can be a bit dodgy (I used to own some Acoustic Energy Aegis 3s- great mid/top end, but the second bass driver merely added slow, excessive thwomp to an otherwise good sound).
Bear in mind that you get what you pay for- a £500 pair of 'normal' 2-way speakers will have better quality drive units than a £500 pair with multiple drivers- and the extra simplicity of the cabinet and crossover design will often give a more natural sound. I've often found multi-driver designs to sound like they're trying too hard.
The main advantages are extra power handling and lower bass from compact cabinets (adding extra bass units lowers the LF response typically by 10Hz per extra unit- but only as far down as the unit's resonant frequency), and also the percieved image of more/bigger being better.
So to sum up, you should choose the best speakers for you, regardless of how many drivers they have...!