Well both have potential advantages/disadvantages.
DSL - The good
More then enough speed for surfing, downloading music, multimedia, etc. You have a dedicated connection via your phone line, so you are insulated to outside factors that could affect speed & performance.
DSL - The bad
Can be pretty pricey (I pay $70 a month). Depending on where you live, and what provider you have, could mean the difference between heaven and hell. Even though you are “insulated” from outside factors (more on this in a minute), there are plenty of things that can screw your connection. Having multiple computers hooked up is ok, but if you intend to have them all in use on the net at the same time, higher bandwidth (a faster dsl package that costs more money) is recommended.
Cable - The good.
Blazing speed, much much faster then dsl. From what I’ve seen prices are more reasonable, usually $39.99 a month or so. Like dsl, quick and easy to set up, and you can hook up multiple computers.
Cable - The bad.
Think of a water pipe coming into a building. In the middle of the night, the water pressure is fine, so filling up the sink and washing the dishes is quick and painless. Now try at about 6:00 PM, right after dinner, when everyone and their mother is washing the dishes. The water pressure (the bandwidth to connect to the net) is much lower, because everyone (the outside factors previously mentioned) in the building has their faucets open! Now depending on how many people in your neighborhood have it, determines how small the pie will be sliced, which can be very good or very bad. Generally, during peak hours of the day, it will be slower, and later at night it will be faster (but who knows? Your building could have all night owls in it).
Both can be good, bad, fast, slow, problematic, maintenance free, cheap and or expensive.
Your best bet is to give us specifics, i.e. Verizon DSL for $59.99 a month or Roadrunner cable for $39.99 a month. I hope this helped.