Some people ride a motorcycle just for the looks. Not for the handling of the bike. Look at the Harleys with the massive back tires.
I think we all know putting on large tires on a 300 will most likely lower handling performance along with making the bike slower than stock. But some of us like that and I see nothing wrong with that.
I personally would not do it. But to each his own.
Well, apparently the 650 has a 4.5" wide rear rim, while the 300 has a 4" wide rear rim.
Other things to consider: The Ninja 650's stock rear tire size is 160. Our Ninjas come with 140, but many have fitted 150 tires, and I think someone has already put a 160 on haven't they? Any bigger than that, I think you might run into clearance issues with the hugger or swingarm. Of course, I'm no engineer, so maybe someone else can confirm this?
That being said, I'll quote Spacep0d regarding the weight of the wheel, unless you have other reasons for wanting to fit the wider rim.