I like the screen fronts, but they need to have a solid bottom at least 12", up to 24", to keep bedding in.
When horses move around or lay down or get up, they kick bedding against the sides and with those fronts, right into the aisle.
We have such strong winds and open doors at the back of the stalls, those let the wind blow bedding all over, so need the standard solid 4’ fronts.
We do prefer hinged doors as you mention.
Sliding doors are good for narrower aisled, but ergonomically bad for your arm and shoulder.
If you have to slide them many times a day and they are not kept in perfect easy to move condition, which most are not, it can give you back or shoulder pains .
If you have to fight with them, as short people do that the handles fit at chest or chin level, swinging doors are better, if the aisle is wide enough for that.
Then, when it comes to looks, if it pleases the one that owns the barn, the rest of us have noting to say, it is her barn to make those decisions.
I will say, those European style stall fronts are very classy looking.
Maybe not for a training stable with all kinds of horses.
Some that may try to jump out, some that may want to “reach out and touch someone”, some that may reach whatever is in reach and chew it up.
It would have been hard to pass a good deal on those stall fronts, they are magnificent.
Any disadvantages, well, they can be managed.