I currently own a registered copy of BBSmart on my 8310, but I've decided to go with a different app. Since I've already paid for it, can I put that app on my wife's 8300 or am I out of $30?

That depends ...............

Does it require a serial/registration code or is it a full version download after purchase.

A full version download would probably work no prob because there would be nothing encoded to your unit specifically. Serials or registration codes are often created (generated) by a user name, PIN or other. This method would/could restrict the use of a software license to a specific device. <This is the norm.

Having said all that; they are both 83** model devices so give it a try ................ it's not going to blow up or anything.

Well, it did ask for my PIN before it provided me with a registration key. I guess I'm stuck with it. I wish there was a way I could transfer it to my wife's phone..

Just send a mail to the developer or where you purchased the app from. handango or mobihand, etc...
Last week i got a new device and transfered my mail viewers progs to the new device. I did send a mail to empower and to mobihand and they changed the PIN for me. Can use them now on my new curve.