I would answer no. 64-bit support in the operating system has been around since Windows XP was released in 64-bit edition, although pre-vista drivers and 3rd-party software were very much experimental. Windows is a fully capable 64-bit operating system.
However, you have to remember that Microsoft's success is built on the fact Windows runs pretty well on any x86 based processor with any other combination of hardware, thanks to HAL. When 64-bit XP first came out drivers were scare in their 64-bit form until traction was gained. As you've observed, most manufacturers still develop 32-bit applications only for Windows; Visual Studio and Microsoft Office proof that it is not only 3rd-party vendors. Why? Ease. Take a walk around any pc-shop and you'll hear all sorts of praise about 64-bit cpus in todays modern laptops but what you'll actually find is that their OSes are shipped 32-bit. It's a standard and it works on 32-bit.
Linux, by contrast, has always been a programmer's platform. Most distributions support at least i386 and "x86-64"; some support ppc architectures. The kernel can be built upon just about every chipset known to man. Why? Linux isn't constrained by needing commercial product stability to survive and is often a researcher's platform. Not only that, but even if the core devs had no interest in porting it, you could. Much of the rest of the gnu system is written for portability so it's trivial to compile elsewhere. And not writing your code in a portable manner isn't considered good etiquette.
Take a look at Flash support in linux - 64-bit alpha. Even Mozilla provide 32-bit only builds although they allow distributors to build official 64-bit versions. Skype is 32-bit only.
Basically, many software developers don't need to support 64-bit yet, or don't see it that way at least. As such, I'd say both operating systems are mature - the eco system around them is what is different.