Depends.
Linux and Unix have, for the most part, been server OS's. A big chunk of Linux is in the server market. Namely web servers and render farms. It is difficult, at best, to quantify an entity as far as use is concerned with a "free" OS.
MS has license sales metrics to fall back on... Linux does not have any of that.
With open source software, a lot of eyes can look at the code and determine lots of things, including security issues, with it. Closed software cannot do such a thing due to the nature of it.
Security issues also are mainly targeted to systems that are the most likely to contain them.
An issue that has a very small percent of people actually utilizing the portion that is vulnerable is likely not to cause any harm or be a target. Linux is, by default, much more secure in the way it handles user accounts and system wide permissions. This makes it "more" secure right out of the box.
Also, someone cannot "reroll" Linux and magically make it closed-source. It does not work that way.

The bottom line? No software and no system is "truly secure"... period.
