To stimulate the conversation I believe that we must first understand what is the main objective of a political "leader". He or she is the marketing of the ideology supported by the elite that finances the candidates and "presents" them to the voters. Staying in power depends on how successful this marketing effort is.
On the other hand the voters do not really know those they vote for. They only have a view that the marketing has served them with the controlled by the elite mass media.
Judging within this context we can find similarities between Thatcher and Merkel. Changing their appearance and even the way they speak is a result of their own conviction as it relates to their projected image.
Thatcher supported the dogma of a United Kingdom that is strong and as independent and competitive towards the European Union. Merkel supports same although she is insdei the Eurozone. Thatcher sent her Armed Forces to Islas Malvinas, Merkel supported the west's operations in Afghanistan. Both of their ideologies are based on the Protestant morals that influenced all western Europe.
Both of their style is simplistic, without sophisticated terminology and very comprehensible, almost a man like style for a woman. We can say for both what was said for the late Israeli PM Golda Meyer that she was the "only man" in the Israeli cabinet.