Your big mistake... and honestly its a pretty common one among techies... is you are worrying too much about what to tell them and not enough about how. I know people and know computers... and bringing the two together isn't hard. You just have to remember that, unlike machines, people care as much about your tone of voice, your body language, your cadence, your word selection, etc as they do about the actual point you are making. They care as much or more about these things than they do about the raw data.
It's a shame I didn't see this post sooner cause you will probably never read this but I have been working as a computer tech professionally for over 10 years. In that time I have discovered that I have a talent for sales and I can make my sales without bending the truth or leaving out important details because my honesty not only engenders trust but my entire attitude and approach is geared toward helping the customer make the individual best decision for their circumstance... not selling the current item that nets me the best commission or advancing my pet agendas.
Make the client feel comfortable that you aren't just telling them what you are because your company demands it of you or you have some fetish towards open source. Care about the clients well being... you're not trying to sell a product, you are trying to help them make the best decision for their selves that can be made. They know their circumstances and you know the industry and when they come to you to show them how the industry can help with their circumstances you make sure they come out on top. The thing is that this might mean telling them to go with a competitors product. This honestly might mean telling them to go with closed source.
Honestly, you have already admitted to telling clients open source is more secure than closed source without having any facts to back you up (or at least none you are willing to show clients). I personally believe that open source is more secure than closed... but I can back that up if I have to and I feel confident my reasoning is sound enough to share with a client. You need to be able to too.
If you aren't willing to listen to a customer and honestly consider their point with the possible result being telling them that closed source is better int their case... then you need to be one hell of a hustler. Used car salesmen in tuxedo type hustler. Otherwise you have already lost simply because MS got there first and the people they hired to get them there first really are that kind of hustler.
In the end it comes down to convincing the customer that your top allegiance (after yourself) is to them. Telling them that will just make you look fake... so you will have to convince them some other way. That is the secret of being good at sales. Having a really good understanding of your clients' wants and needs and being knowledgeable enough to sound like you could write books on the subject your discussing are both major pluses as well.
Also... though im sure it was said in the avalanche of text that came before me... point out two things to the clients. First off it is not possible to "prove" that a product is more secure than another. There are factors beyond imagining involved in a product being or not being secure. Thus them asking for proof is from you or from the MS people is not easy to come up with an honest answer that is very convincing without first explaining a number of things.
As for what to say... start the theory behind why open source is more secure. Theories are not proof but when you get right down to it there is no proof that the faster you move through space the slower you move through time... but we have theories and those theories are themselves backed up by evidence. Those theories have been applied time and time again in the real world to create working technologies like microwaves and electron microscopes. And these theories point to the slowing passage of time in any cased where the passage of space increases. From there move into statistics. Statistics are also not proof, but they are a good indicator of trends and make empty theories look like they are more than just theories.
The theories behind why open source should be more secure are sound and the statistics back that up. All you have to do is package that message in a way that convinces client and makes them feel at ease.
Also, it would probably help to use MS's tactic against them here and point out that, while the source code being available might make it easier for hackers to find exploits, it also helps those who want to make the program better find them too. Point out as well that if an exploit were to be found before it was patched that because open source is open it would likely be fixed faster as well (more statistics on that subject would be good as well). Answer the questions as best you can and, if the client is really worried about it, offer to find the answers to the ones you can't (if your company will allow that, I suppose that depends on how badly your company wants to keep clients). Have a ready made template email with links to the statistics and alternate source of other studies that show similar results ready to go and offer it to the client.
Simply put, treat it like you would an up coming sales pitch. You know they are going to call. Be ready. Be professional. Be the clients ally in the war on hackers. Don't let doubt show up in your voice, your body language, or your wording... you are right and they should listen to you. Otherwise why would they? They need help and you can help... and will if they want you to.