I've tried both over many decades of hard use with braid & leaders. The main drawback to the double uni knot is bulk. This bulk seems to "click" through the guides on the cast & retrieve. This "clicking" equates to wear, reduced casting distance and less joint strength - in my opinion.
Some of my fishing friends do use double uni successfully however, so it may just be a matter of preference and confidence, more than actual joint strength. In any case I prefer the Alberto. Less bulk, creating a more streamlined knot, which actually isn't a knot at all, but rather a braid. Sort of like the old Chinese handcuffs, or finger cuffs, that you use to get as a prize in Crackerjack boxes.
I've never had a failure with a properly tied Alberto. And in the TV series entitled, "Knot Wars" a few years back, the Alberto had superior static knot strength over the double uni. These were under very controlled conditions however and the difference between them was less significant. I don't believe that you can go wrong with either, provided you take the time to tie them correctly. And if you intend to stay with the double uni, I'd advise you to re-tie more often than you think you might need to.