I live nearby and have been in Pirosmani for countless number of times since it was opened (and that was a looong time ago). The main problem, in my opinion, is that they alter their quality and portion sizes from time to time. You can have a good and big enough meal one day, then you can have a noticeably smaller one but just as good 1 months later, and then you can have a big and bad one (mainly they use cheaper and lower quality meat) in another month. Sure it's not a restaurant, but the quality should be consistent. Want to make more money? Well, change the prices but don't touch the food. If people like it, they'll come back.
I know the restaurant owners - they are all Georgian (the main ones moved back to Georgia some time ago) and have at least 3 other "restaurants" (another Pirosmani, Suliko and Kamikaze). I would say that Kamikaze has less issues than any other mainly because it's near another place called Lowenruh which cooks pretty-much the same stuff. They are competitors, so this affects the food in a positive way.
As a conclusion - if you haven't tried Georgian food and just want to eat without spending much - you'll probably like Pirosmani. But if you are into more qualitative stuff or just a gourmet - there are many good restaurant in the center of Tallinn. But be prepared to pay 1,5 - 2 times more than you might have paid in Pirosmani.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.