Let me preface this by saying I have used every major 3D package at some point extensively except Cinema 4D and my preferred software is Houdini. I also have a grudge against autodesk as a company so my view is pretty biased 
I haven’t touched Blender in about 8 years. I see people do good stuff with it, but based on my previous experience, never likely to touch it again.
Modo is a great piece of software. You look at Max or Maya or even (now defunct) XSI and they are more similar than they are different. Modo I think is decidedly different in that it obscures to a greater degree some of the ugly lower level technical aspects of 3D modeling in favor of artist friendliness and intuitiveness. To that end, it has some really great modeling tools you won’t find anywhere else. To it’s detriment, it was engineered with more of a film and video mindset and you will encounter idiosyncracies you sort of have to work around making game content in Modo. I know some very skilled professional modelers and they almost universally prefer Modo. I can’t speak to Modo’s animation or rigging tools because I don’t use it for anything but modeling.
For Houdini, I don’t think there is anything it doesn’t do well if not better than anything else out there. It’s modeling tools on first blush might seem primitive compared to something like Modo, but they are extremely powerful and well suited to game development. The hurdle with Houdini is that it is fundamentally different from any other package out there and doesn’t try to hide any of the deep technical aspects of computer graphics. The tools are very general purpose and you need to usually combine a handful of operators to get the same result as another package. The upside to this is it is non-destructive and for the most part you can go back to any point and make changes that will filter down to the end result of your models. It’s also easy to proceduralize your modeling, say build a tool that spits out hundreds of variations on rocks, or doors or walls. It’s definitely not for everyone though. The learning curve can be steep.