Well, casuals will most likely go for the Wii version of multiplatform games like Tiger Woods/Madden/Active Sports/whatever over PS3 versions. They don't care about graphics, or they'd have bought a 360 or PS3, not a Wii. Plus, the Wii version of such multiplatform games will be cheaper than HD versions. And finally, the installed base, casual-wise, is like 100:1 in favor of the Wii, compared to PS3.
Wii was built from the ground up to appeal to casuals. From its very inception it was meant to be universally understandable. It's simple, extremely user-friendly, and appealing. That's why its interface is made up of channels, and why its controller is shaped like a tv remote, with very few buttons, among other things. It's marketed to be, literally, for everyone.
Imo arc (or whatever it'll end up being named) is going at it in the wrong way. It's not like casuals will flock to the system simply because it has motion controls. It's a combination of appeal (and let's face it, the Wiimote is much more appealing, intuitive and easier to understand than the Arc. Just look at the latter, if you don't know what it is, you're like lol whut?), the right software, and ease of use. Imo arc does nothing to truly appeal to the casual user, besides offering motion controls. That's not the only thing needed. There's much, much more to the success of the Wii than that. Whether arc's controls are more precise or better implemented or not doesn't matter to the casual user.
As for 'core' games, we'll have to wait and see, but honestly, it's not the hardcore Sony are after with this. They don't need to be convinced, least of all with motion, that PS3 is a system for them.
Imo, Nintendo doesn't have anything to fear from arc, at all. It could even end up making the Wii more popular, because people (read: casuals) will compare the two, and decide for themselves which is more worthy of their cash and attention (and a lot will, imo, still pick Wii, because of the points I listed above).