I've done this a lot, on my own basses and on customers' basses. You lose the five highest notes on your G string, and gain the lowest five on the B. This is an outstanding deal, in many cases. A few things to bear in mind.
Some four string instruments don't want to hear a B string. It might be the lower mass or stiffness of the neck, or the way the builder "voiced" the bass. Unless your name is Tobias or Turner, you really won't be able to tell until you try it on your bass. No one you encounter on any web site will be able to predict whether you will like theresults or not, or whether your instrument will support an acceptable B string or not. Don't expect a computer to predict the future. Go buy a five string set and get it on!
Most four strings have 34" scales. Most of the best fives use a longer scale length, around 35". The increased tension necessary to get equal gauge strings up to pitch on a longer scale seems to produce a more solid B string. Don't expect too much past the seventh or eight fret on the B, as the tone tends to get a little choked there under the best of circumstances. If your bass has a scale length of less than 34", your chances of being pleased with the results decrease. Consider using a heavier gauge string unless your bass has a scale length longer than 34".
Most often, the G string on a given set exerts more tension on your neck than the B. You may have to decrease the truss rod tension after the switch, otherwise the decreased tension of your BEAD set may result in less relief or even a little back bow. This is a quick fix, and if you use the next heavier gauge set, you may not even notice it.
Your nut slots may need to be widened by a hair. Not deepened, but widened just enough so that the heavier gauge strings rest in the bottom of the slot. This is a very simple operation, but you can also wreck your nut by getting the slot deep enough to cause string buzz in the open position. Most basses have enough clearance in the slot width to accomodate a slightly wider string, but if you notice unusually high action at the first fret, or if you encounter tuning problems (especially pinging) with your new strings, he slots are probably too narrow and need a little attention. This is a job best left to a real repairman, but don't let this dissuade you from the great experiment! If you need a little set up work after you take the plunge, the cost will probably be less than $50 and the results will be worth it.
The BEAD set will be a heavier gauge than your EADG set in all liklihood, so a little intonation adjustment will probably be in order. You can hold off on this until you get it strung up and see how it sounds. No biggie.
I've done this to an MTD 435 (a 35" scale four string) and the bass just slays. It is a blast to play (nice narrow neck), it sounds tremendous, and it largely eliminates the need for a four and a five string.
Turn off you computer, go buy some strings, and report back your results!