We own both the Jambox and the Soundlink.
They are both great devices. The Jambox (even the Big) is more portable than the Soundlink.
However, the Soundlink has better room filling sound than the Jambox.
We basically use them this way-
Jambox for bopping around; it is so easy to just take with you.
Soundlink more at home stationary use.
It would be nice if the Jambox (don't know if Big made this change) could connect to more than 2 devices. The Soundlink can connect up to six devices. Also a nice touch is how the Soundlink shuts off when you close the leather or cloth (depending on model) flap. It uses a magnet like the smart cover. Nice touch for the Jambox is you can take a call on it, while the Soundlink left that feature out.
Both are very nice. Best thing it to go listen and feel both.
Hope this helped.