The first solution is the easier one : you just have to handle the pause / resume event of your application, and everything will work. The application will nicely close, and restart with the new Layout.
As you HAVE to do this for other interruptions ( like a phone call while the user is in your activity), it means it is no more work for you.
The second solution is trickier, as you have to handle everything by yourselve, and be cautious about memory / resources leaks. But it allows you to have faster and/or nicer transition !
Google engineers highly recommend the first solution !
There is a very interesting blog serie on this subject here :http://androidguys.com/?s=rotational+forces&x=9&y=9
Note on the part 3 ( the more interesting for you ? ), there is a comment from a google engineer on this very subject !