Taj Mahal at night:
Shah Mosque at night:

Shah Mosque at night:

Buildings like Taj Mahal are called "Kushk" in Persian, the English word "kiosk" has the same origin, Kushk is in fact a great lone building in the middle of a garden which can be accessed from all sides, of course the most important thing about these buildings is symmetry but almost their whole beauty can be seen at the first glance, hijab in the Islamic culture is not just about women, Shah mosque is a beautiful women with hijab.Taj Mahal has a sense of symmetry + its style is more minimalist. I really adore that.
The Badshahi mosque can not be compared to the Shah Mosque, that is just large, the central dome of Badshahi mosque is just 15 meters high, like a simple mosque.symmetry of the Taj is unmatched!
The Badshahi mosque (Lahore) would be better compared with the Shah Mosque (Isfahan).
Symmetry + the building being the centerpiece "jewel" rather than a utilitarian collection of rooms is the "Indian" contribution to the architecture of the Taj.Taj Mahal has a sense of symmetry + its style is more minimalist. I really adore that.
A Persian style building in India can be really beautiful, there are several ones of them in Iran, white marble is a beautiful stone but there are some shining stones which are more beautiful than it, for example look at this one which seems to be both blue and green:Taj Mahal is quite simply the most beautiful building in the World, its just sublime.