DSL
DSL has lower overall bandwidth than cable, hands down. The highest I've seen it advertised is in the 6Mbit region, and you pretty much need to live less than a wire mile from the CO. The upside with DSL is that in a properly provisioned network, bandwidth contention won't be a big deal. In a poorly provisioned network, the carrier will use a cheesy DSLAM with 100-1000 DSL lines sharing a single DS1.
With DSL, you do get your own line with its own line card (usually) in the CO. Your traffic generally cannot be seen by other subscribers.
DSL performance varies greatly. The speeds initially available to you depend on how close you are to the CO in "wire miles," not easily measured by drawing a radius from the CO to you. DSL is also noisy - it can interfere with neighboring lines in its wire bundle and is itself prone to interference. The dynamic nature of copper wires in the ground or on a line is another variable - they expand and sheink with the temperature and are sensitive to the many ways of splicing them. A copper line is typically spliced multiple places and many of the passive devices placed on the line to optimize voice performance hinder DSL performance.
Ever notice how reliable that dial tone is? Keep in mind that telcos are the force behind DSL, and your DSL signal runs over and through facilities that they own. The DSL outages I've had have been short, and usually related to my own equipment (doh!).
Cable
Cable has greater bandwidth than DSL, but it's a broadcast network somewhat like an ethernet hub. Some providers will quote 12-15Mbit, but that bandwidth is shared with everyone on the same segment, node, local loop, whatnot. You might be lucky and have only a handful of data subscribers on your segment, or unlucky with 90% of the customers also having data. That neighbor of yours that streams dumb video clips all the time like PC "multimedia" is still something amazing of itself is partially responsible for your sub-modem speeds on "superfast" cable.
With cable, you get a shared line. All your data is (potentially) seen by all other subscribers. I don't know if DOCSIS or other cable systems provide for encryption of all data on the network, but another subscriber could tweak his modem to capture all packets of interest.
Cable performance seems to be more steady than DSL performance. It uses a decent-quality coaxial cable that is shielded from interference. The coaxial medium has greater bandwidth than unshielded twisted-pair copper.
Cable reliability is a crap shoot. I've had a few lengthy outages (1-4 days) caused by the cable company and they didn't seem to care. From what I've gathered, the outages were in their distribution or core layers - more concerning than outages in the access network since it involved routers and other things that should be more reliable if operated properly.
Fiber (also shamelessly plugging my employer)
Fiber has greater bandwidth than cable or DSL. There have been a number of fiber rollouts in the country - most of them have been small-scale experiments using proprietary equipment. Unlike cable and DSL, the bandwidth in fiber can be affordably increased simply by upgrading the active equipment at either end of the line.
Verizon's rollout of fiber to the premises (FTTP) is based on standards developed and published by three of the large local carriers. Thus far, only Verizon has begun a network rollout based on these standards.
With fiber, there is typically an active component in the CO that has line cards - each of which connects a number of subscribers (generally under 50). The fiber is then brought to a hub in the neighborhood where the fiber is split. From there it runs to each individual subscriber's premises to a fiber terminal. At the fiber terminal, optical:electrical conversions are done and familiar connectors for voice, data, and video are present. For data, there's a 100Mbit ethernet jack that's typically wired to a jack in the house that a router connects to.
The fiber line is shared, but the individual data speeds sold on the network are nowhere near the total speed present in the line. If all subscribers bought the maximum speed, the subscriber bandwidth:line bandwidth would be around 1.5:1 - nothing like how cable is oversold. The bandwidth provisioning in FTTP is more like how a business network than a consumer network. VZ's fiber network is a possive optical network (PON). All data on the network is encrypted. In theory, someone might be able to sniff all the data his optical terminal sees, but the optical terminal is telco property and bolted to the side of his house. Control of the terminal is out of band and must come from the optical side. Hacking a fiber terminal would be a tremendous challenge alone were it not for the fact that network ops is constantly monitoring the fiber network, and that the fiber terminals won't work if tampered with.
Fiber is immune to almost all of the environmental factors that effect DSL and cable service (with the exception of "digger fade" caused by fiber-seeking backhoes).