Whether an antivirus is free or not has almost no correlation with its quality. The theory is that when an antivirus is expensive, then the vendors have more money to spend on maintaining the antivirus, and, given the theoretical impossibility to reliably distinguish virus/malware from non-hostile code, an antivirus can be effective only if it is continuously tuned and augmented, on a daily basis.
The theory breaks down on two points:
That the paid vendor makes money does not mean that he wishes to spend it on making a good antivirus. The ultimate goal of any commercial venture is to make a profit, so the vendor will prefer, all other things being equal, to pocket the money rather than spending it on exhausting antivirus maintenance. In theory, market pressure should evict antivirus companies of poor quality; however, it is known that the software industry is full of de facto local monopolies because of technical details (switching from one software to another incurs a noticeable cost, so competition is not fully effective at lowering prices).
The free vendor may be sponsored. An example is Microsoft's Security Essentials: it is in the best interest of Microsoft that Windows users don't get bogged down by malware, so they fund the development and maintenance of a good antivirus that they then give for free (it is now included in Windows 8, which is why there is no separate "Windows 8" download).
Banks sometimes sponsor antivirus packages for their online banking customers, since it is in their interests to ensure the security of their customer's computer, as the bank may be liable for some or all of any losses.
Either way, maintaining an antivirus is labour intensive and security engineers must be paid somehow. Free things are not actually free to create.
It may be possible that any specific third-party non-free antivirus offers some extra functionality which, from your point of view, makes it worth the cost; however, if you don't see it by yourself, then chances are that a free antivirus will be fine for you. Potential distinguishing qualities include ease of deployment in large infrastructure, scalable email scanning on the mail server, and other business-oriented features which are usually not relevant for home users.