Perhaps another way of putting how I see it - excluding really heavy traffic like video or (cough) torrenting linux isos (cough), you're rarely saturating your broadband bandwidth with casual internet use. Whereas with dial-up/non-broadband, it didn't matter what you did, you were saturating your bandwidth and always waiting.
(YMMV - this is just how I see the term 'broadband' as a qualitative label)
After a certain point the thing rate limiting you for most network usages (including web browsing) stops being your own connection to the ISP and starts being other things, like the speed of the website you are visiting under whatever load it is currently under, the website's own bandwidth out to the greater world (split up among however many people use it), etc.
I currently have 300/20 service, and though I see a nice set of numbers when I visit speed testing sites, in typical real world web browsing situations it feels no faster than the old 30/5 service I had before this.
[0] http://arstechnica.com/business/2015/01/fcc-chairman-mocks-i...