Option 1 mostly works, providing you're going from external to external. Usually the consolidate causes more trouble initially since you have to be very careful to set everything up just right. It's almost better to copy the files, delete the library, and start over.
Option 2 - sometimes. It depends, of course. A lot of people go from using the 'My Music' type directory to 'Music' or something (without thinking about it).
On removable, I found that Songbird Portable handles this well by substituting the drive letter on the fly, so if my external is D, or E, or F, it doesn't matter as long as it's the same path (/portableapps/documents/music, for example).