Measuring the security of a specific piece of software is not an easy task. There are tools which do this, however mostly depend on access to the source code. In the case of a browser the situation is a bit simpler since it is easier to test against fuzzing tools - however this will be part of standard testing for mainstream software so the results may be inconclusive.
The arguments regarding open versus closed source have raged for years - and a strong argument put forward by the closed source incumbents is that since their products are much more widely used, then they will therefore attract much more attention from people trying to compromise the product. However this is an argument which no longer applies to MSIE vs Chrome vs Firefox. And MSIE's historical record on security shows it have had many more reported and serious vulnerabilities than Chrome and Firefox.
But while it's difficult to measure the security of a piece of software, it's simpler to measure many other aspects of the quality of a piece of software - especially where it has been written to a well defined standard. Again MSIE (historically) compares poorly on both performance and standard conformance when compared with Chrome and Firefox.
A further consideration is the effort required to ensure that vulnerabilities in the software are fixed. That doesn't just mean the vendor providing a fix, that means getting it installed across the user base. Chrome is particularly good at upgrading itself transparently.
As others have mentioned, MSIE is deeply tied into the underlying operating system. Which makes patching a complex process.
And of course there is the underlying economic model. While MSIE, Firefox and Chrome are all free (as in free beer) the underlying financial models are very different. It just does not make sense for Microsoft to maintain products for a long term - especially so when it's as tightly integrated with a whole operating system. And Windows XP is getting to the end of its support lifecycle. Upgrading an operating system is a lot more painful than upgrading a browser - and the software architecture of Chrome and Firefox make it much easier to have the most recent (and therefore the most secure) product available for use.
Dr. E. D. V. Nunez' letter discusses the wider economic and social importance of free, open-source software far more eloquently than I can.
Then there's the question of all the other components which go into making a browser. One which has been discussed quite a lot recently is root CA's bundled with a browser. IMHO, all the major vendors serve their customers poorly in this area. However in Microsoft's case there is far greater likelihood of a conflict between it's interests and those of the user than for Chrome and Firefox.
A further consideration is the bundling of services with the product. In the case of a browser, particularly one used for webmail, good phishing detection should be a prime concern. IME, Google's service (implemented in both Firefox and Chrome) is much more comprehensive and more quickly updated than that of MSIE.
At the end of the day, while experience has taught me to be very careful about ipse dixit, if your opinion is being sought, then there are limits to which you should go in justifying that. Just as conversely, I wouldn't tell a heart surgeon what the best kind of stent is, I assume that she has some knowledge of the subject which is part of her value to society and would be difficult for her to impart to me without a great deal of time spent on this by both of us.
Where we don't have enough information to fully evaluate opposing arguments, then a reasonable solution is to look at the people arguing the cases and consider how they would benefit or lose out by presenting a misleading case. We're back at economics again: it costs a lot of money to write a browser, Google and Mozilla get no direct benefit from doing so. Microsoft does.