All "Internet" access involves shared infrastructure at almost every step. When it comes to "the last mile," with traditional DSL, you have a dedicated line to the central office, but thats it. Fiber to the Node, you have dedicated access to the neighborhood node, whereas cable is basically shared all the way to your cable modem.
Because shared infrastructure is always involved, the important issue is the network engineering and capacity planning. At this late date, if you are suffering from frequent congestion that is obviously tied to the last mile, then the provider is either doing a shitty job with managing their network, or the standards they are managing to are horrible. I am sure that you won't find a provider that will admit to either of those things.
I stuck with DSL for a long time because of better price transparency, and, at least historically, higher standards for network engineering. I finally gave up on it though because the cable co was so far ahead while the telco seemed like it would take forever to deploy FTTN upgrades that would allow me to get faster access than the 3 Mbps up / 768kbps down that I'd been stuck with for the better part of a decade. I think the economics of modern cable-based data networks are more favorable and make it easier/cheaper for them to expand capacity and manage hotspots of congestion.