For an Internet user there are two basically two measure of bandwidth. One is the backbone connection of your provider and the other is your modem connection to the provider.
The ultimate factor of connection speed will always be the user's connection speed to the Internet provider. The user's modem determines the top speed of all transfers.
The speed of the provider's backbone connection also becomes a factor to Internet throughput in certain circumstances. Generally, the provider's backbone will be at a much higher speed than most user's modem connections and so, under ideal conditions, the user will get close to the maximum throughput of their modem.
The Internet, in general, uses the principle of sharing resources among many users. Thus, an Internet provider can service many more people (throughput wise) than the raw numbers would indicate. For instance, if a provider has a 128K bits per second Internet feed then, according to the raw numbers, this feed would be "maxed out" with four users connecting at 28.8K bps. However, since any one connection is rarely used to capacity, the 128K feed can be shared among many more than 4 users at the same time and all will receive acceptable performance although there may be periods of increased activity which will cause delays. All Internet service providers operate under this sharing principle.
Under ideal conditions, a user can expect better performance from a provider with a higher speed feed. In reality, however, conditions are very rarely ideal. If a provider has a T1 feed (~1.5 megabits per second) but severely over subscribes the feed, then performance could be worse than a provider who carefully manages a slower feed. In casual testing, very little performance difference was found between a provider using a 128K bps feed and one using a T1 feed.
Apart from these connection speed issues, there are many other factors impacting the performance of Internet activities. When connecting to a remote service, one must take into account the speed of the remote connection, the load on the remote server and the amount of traffic on the Internet between the user's computer and the remote host. All of these factors could combine to reduce even a T1 to a slow crawl.
In the end, the only way to gauge the performance of different providers is to try the connections and actually "see" the performance. While the raw numbers would indicate an advantage for a provider with a higher speed feed, the realities of the Internet tend to even out the playing field for different speed feeds.