@Polynomial makes very good points regarding "security through obscurity" and you definitely shouldn't secure yourself based on "obscurity" because it has proven not to work. However, I don't believe that the answer to your question is that simple - I think your question is more of a "risk reduction" question but could be wrong.
Quite often in the security community, we simply say "no". Choosing something because it's not "popular" or doesn't have as a big a market share, however, isn't a straightforward "no" imho.From your question, imho, I don't believe that you are suggesting a "security through obscurity" policy.
I have seen examples of people employing a successful strategy using "less popular" software. It is important to note though that it's quite often a short-term solution, very much not a long-term thing.
I'm pretty sure that it's a fact that the vast majority of attackers will target the technology that is used by the majority of the people, that's generally why Windows, Internet Explorer, Adobe Acrobat were all targeted (as well as the fact that some of the code was very poor). Later Windows and IE (IE9 is significantly more secure) releases have been dramatic improvements on their predecessors from a security point of view both because they've taken such a tanking from attackers and the security community as well as losing market share (possibly more hurtful). However, despite these security improvements, Microsoft is still targeted, Patch Tuesday is still quite often "huge" and it's because of their large user-base (a big target).
For example, I know of people who moved from Windows to Mac because it had less market share and was deemed "more secure", remember the Apple campaign.
As Apple have become more popular, they've been targeted much more and there is a lot more malware specifically for MAC now then when it wasn't as popular so surely that would confirm your suggestion, that yes it was more secure when it wasn't as popular. It's not the underlying infrastructure that's made it more insecure but generally all the nice apps that Apple adds on and it adds these on to please users, mostly new users who aren't as technical as its original user base. It's not to say they were "more" secure before Steve Jobs took over the world but I believe it's safe to say, that you were less "at risk" from being attacked using a Mac 6-8 years ago than you are today.
I know folk now moving from Mac to Linux to remove themselves from the Mac "attack surface". Whether Linux will become as popular as Mac on the desktop is another question but there are many reasons why using Linux as desktop is secure (too many for here), not least because the person using Linux is most likely technically savvy and aware of the risks) but "less popular/less of a target" can be one of them.
Similarly with Adobe, their software was attacked because of the huge target base that a successful exploit could compromise - there are vulnerabilites in other PDF software but they weren't attacked to the same degree (were they?). They're still being attacked because it's the predominant solution for reading/writing PDFs and vulnerabilities despite securing their software so much more (e.g. their sandboxing technology)
I know of plenty of folk that use Opera or less popular browsers for browsing certain important sites because whilst there are vulnerabilities in that software also (as there is in all software), they're not as well known or as well targeted. You are much more likely to receive an email with a link to a web-site that contains a payload to exploit a Firefox, IE or Chrome vulnerability.
@Pepe also makes a very good point regarding ensuring the software that you are using is maintained and regularly patched (Opera certainly is). I'd also add ensure it's a reputable project, do some digging on the Internet to check out the community/person behind the software - Sourceforge is awesome but it does host some "interesting" stuff to say the least. If in doubt, ask on Security Stackexchange :)
In summary, I don't think it necessarily makes you more secure but if you have your head screwed on, are aware of the risks etc then I do believe such a philosophy can be used to successfully reduce your risk, if used correctly as part of an overall defence-in-depth strategy and you don't rely on it totally.