The "open-sourcing" of PhysX has been widely misreported. It is still proprietary. The source is on GitHub, but it's only available to developers with a GameWorks account and isn't under a FOSS license.
If the source for the SDK is available, what part of PhysX isn't available? All of their core algorithms and solvers are available, although the Flex source code isn't available.
Game works is another kettle of fish thigh.
Not all solvers are available, GPU solver's aren't, FLEX and APEX are also currently not available.
FLEX source won't be released as far as i can tell APEX will be released in some form or another in the future.
The basic CPU solvers are there, but the license doesn't really allows you to modify them anyhow.
PhysX isn't Open Source only the free SDK is, all the stuff that actually makes PhysX work is proprietary and is part of NVIDIA GameWorks.
Havok isn't just a physics engine although Havok Physics is probably the most used middleware that Havok makes.
Which is better well it depends, PhysX is supported by more 3rd parties, but you can only have dedicated processing on CUDA enabled GPU's, PhysX supports both AMD and NVIDIA GPU's and probably in the future Intel and maybe mobile ones.
Overall more games use PhysX these days than Havok, it was the defacto standard in the previous decade but not so much today, I don't think a single game came out this year which uses Havok.
Many of the big hitting AAA games use Havok. Although they haven't launched yet, assassins creed, fallout, Halo, just cause 3. There were plenty last year like Destiny, watch dogs, evil within, shadow of mordor.
To briefly answer your question directly: until a while back Havok had no GPU acceleration, where PhysX had GPU acceleration on NVIDIA cards only (best-effort on CPU for other GPUs). It made sense to always use PhysX because it was comparable to the competition on other GPUs but always better on NVIDIA.
It is now likely better to always use Havok FX (which runs on many GPUs), but PhysX had a time lead resulting in it being entrenched as well as being more mature.
The PhysX SDK is also free with immediate download[1] (causing indie devs to more likely use it and blog tutorials about it). Havok has a price tag, but also has a indie program called Strike that has an undetermined (inquiry-walled) price tag.[2]
