** can ride offroad, panniers almost impossible w/o breaking something. if your load is not too heavy you can actually do some pretty extreme off-roading - i'm ridden downhill sections with the Bob and maybe 35-40lbs(15-17kg) on weekend trips in the Alps where other MTBers were walking their mountain bikes...
** less wind resistance if you have head or especially cross winds
** more stable at high speeds although you have to learn how to pack the weight - i did a 5-day trip on the Northwest coast with a friend with panniers and downhill he had to ride the brakes and always dreaded the downhills while i cranked to increase speed!
** easier to unhitch, lock up the trailer and your stuff and do a trail ride w/ racks or whatever
** loading your bike onto a train or into a hostel or whatever can be more difficult with the BOB - although it can be easier... the BOB definitely takes up more space in a bike room unless you detach it but then you have 2 things to carry and have to worry about leaving one unattended
** BOB puts less stress on the bike and requires less maintenance - also as someone else said, you need a good bike and frame for a full-load w/ panniers and with the BOB it's not really important
** no problem with front or full-suspension - front suspension pannier mounts exist, but they can be difficult to find and set up - full suspension and panniers (no idea if that works)
**more places to put things: e.g. knife is in front of left front pannier, etc.
** can be easier for train or something where you have to walk the bike
if you're doing any off-road, BOB wins hands-down. OR if you have front suspension or full susupension, it's also way easier...
For road touring, it's a mixed bag - you have to learn how to pack the BOB - so you can remember when everything is b/c it's just one big bag and and so you can get to the items you need easily without unpacking everything and to get the weight stable...
but i think for road touring neither choice is bad - just different
i've been really happy with my BOB and on my tour with my friend w/ panniers i usually felt i had the better setup except when i had to pay for 2 bikes on the train b/c they counted the trailer as a bike (b/c it has a bike wheel it's not luggage). i also had a little more trouble when pushing the bike through heavy pedestrian crowds b/c of the length