Having looked at a variety of parliament buildings from several different countries these are the common themes I have found
Differences throughout existing Parliament Buildings
Evolve from Gothic to angular but still with influences from previous parliament buildings, eg. Columns and arches
Problems with the site based on required building
The size of the site will require a many storied structure so as to fit all the required functions into it.
Also many of the surrounding buildings are historic so it would be difficult to obtain planning permission but also the structure would have to remain within the footprint of the building already in place.