AT&T is currently calling HSPA+ 4G, and this is going to cause a lot of confusion when AT&T rolls out its LTE network, which is more of a true next generation protocol. What causes the confusion is the difference between the SPEED of something, and the true generation change.
You can have a HSPA+ connection(which is based on 3G technologies but has been upgraded to provide higher speeds) that runs at 15mbps, and you can also have LTE running at 15mbps. As a result, even though HSPA+ is really an evolution of 3G, it was initially being called "4G speeds", to distinguish it as being different from LTE, which is considered a fourth generation protocol.
They did this because T-mobile was calling it's service 4G when it clearly had no LTE network in place, and AT&T was not ready to launch its LTE/4G network yet(due this summer)
On the Verizon end, they DO have LTE/4G available, but only in select markets, so most people wouldn't have 4G service, even if they had a LTE/4G phone. In general, the AT&T 3G service is faster than Verizon 3G service, but Verizon has a larger network than AT&T, and in many areas, has better service levels, so the perception is that Verizon is better.
So, where is the truth here? It is a bit of all of this put together. There are areas around the country where AT&T has better coverage, and other areas where Verizon has the advantage. AT&T has had a bandwidth shortage in some areas caused by iPhone users using far more bandwidth than those with other phones, and this has led to a quality decrease for AT&T users in the affected areas. GSM and derived technologies really would provide the same quality of service in general compared to CDMA, but if you are in an area with poor service, it doesn't matter which you have, you have poor service.
It should be noted as well that because Verizon is the local phone company in many areas, Verizon has been able to put up cell phone towers on the same land, and I don't believe that regulators have addressed the issue of Verizon getting government subsidies to maintain the phone lines and equipment, but using those same subsidies to improve their cellular network since they are linked.