You can easily check the speed of fetching an individual piece of content. I check frequently on my projects that pages are served up fast (sub 200ms). In general, it's as fast or faster than it ever has been. You can also test your max theoretical throughput by running parallel GETs on the same piece of big file content (using a "download accelerator").

I suspect you're confusing perceived speed with actual speed. The web is much richer now (as you mentioned). Flash, Javascript, and CSS wreak havoc with rendering time. Browsing the web with anything less than a ~2 year old computer is going to feel a bit sluggish these days. Even with a modern computer it's not going to be as fast as the largely static web of the old days.