I've tried both. We often find we need to move the key of a song up or down a few semitones and the lower tuning is helpful when the bassline is already at the bottom of the range of conventional tuning.
I had an OLP MM3 5-string for a while but couldn't really get on with it. It wasn't a bass I'd want to spend all night playing.
I then strung a bass up B-E-A-D and just used it for a small number of songs in the set, but swapping basses during the set was a load of unnecessary hassle and I couldn't bring myself to play it all night. Having a 2-octave neck helped with the higher octave stuff, you just end up playing everything in the top octave up a 4th. The only problem I had, which may have been specific to the bass, was that it didn't trigger the synth pedal very cleanly.
Then I found a 5-string that I was comfortable with playing, that I do want to spend all night playing, did trigger the synth properly and as an added bonus it has a huge range of different tones. So I'm using that as my main bass now and getting into it. There is still the occasional 'Where the hell am I' moment but they're becoming fewer.
As others have said, I'd recommend you give BEAD a go, unless you want the excuse to buy another bass. Who, me?