Copying ibdata files around is fraught with danger. Important bits of metadata can be stored in other files such as ib_logfile0 and ib_logfile1 (this is not a comprehensive list) and the settings on the new server (such as the size of those two logfiles) needs to be exactly the same as the old server. If you get any of this stuff wrong or miss copying one of the files, the new server will not start and you will have to deal with MySQL's helpful error messages in the error log.
Xtrabackup handles all of this for you. After you use it to dump your data and "prepare" it, you can do a straight file copy to the new server and start it up with the new ibdata file. The "prepare" step takes significant time.
However, since you mentioned that the database you are moving is only 100GB of the 250GB ibdata file, I suspect it will be quicker using the mysqldump method simply because it only has to transfer 100GB of data instead of 250GB.
You can pipe the output of mysqldump straight into mysql to avoid having to save the dump to disk like this:
mysqldump -uusername -pmypassword MyDB | mysql -h server2 -uusername -pmypassword MyDB
The mysql client has a -C option that enables compression if both ends support it. Just put it in before the -h option. The transfer over the network is likely to be the slowest part of the whole operation.
If your server doesn't support compression, you could do the transfer via ssh with the -C option instead:
mysqldump -uusername -pmypassword MyDB | ssh -C server2 "mysql -uusername -pmypassword MyDB"
Last thought: The time it has taken me to write this is probably longer than both methods put together unless you have a 10MB/s network. Get it started. :-)