Is there an advantage to use decision trees in OneVsAll than using "classical multiclass trees"?
In general OneVsAll is a device useful when you want to transform a binary classifier into a multi-class one. This happens when models cannot handle multiple classes or when it is difficult to adapt it. By doing so, you have to normalize the probability estimates, otherwise they are not too useful, being rather non comparable. That alone is probably a sufficient reason why nobody use this when a multi class version is available.
There are cases when something similar might be useful. For example when you have a lot of classes. One might try to group the target levels, build a classifier for groups and later do subsequent classifiers for each group. But there are not overlaps between predictions.