Here's what's likely to happen in Egypt: It will evolve into a Turkish-like government with the civil side adopting a pro-Islamic stance, while the military makes certain the place doesn't turn into Afghanistan under the Taliban.
Egypt was, for a good portion of the 17th and 18th centuries, part of the Ottoman Empire which was distilled into modern Turkey by Mustafa Kemal Atatürk.
The Ottoman Empire, which at its height in 1699, stretched from modern Romania in the north, to modern Tunisa in the west and down to Yemen and the UAE in the Arabian peninsula.
In 1923-ish Atatürk overthrew the Sultanate of the Ottoman Empire and created the modern Turkey with a series of secular reforms. According to the BBC:
"These reforms included the emancipation of women, the abolition of all Islamic institutions and the introduction of Western legal codes, dress, calendar and alphabet, replacing the Arabic script with a Latin one."
Egypt, under Hosni Mubarak, has maintained its amalgam of Western and Islamic traditions.
Having spent a good deal of time in the Middle East over the past 20 years, watching old Egyptian movies has become a favored past time. I can't understand a single word, but the plots of the broad burlesque quality of the comedies and the dark film noir values of the dramas remain easy to follow.
Just about every movie had at least one scene of scantily clad women belly dancing to the delight of patrons in gaudily decorated nightclubs, Sheikhs in gaudily decorated tents or, if the budget was large enough, both.
That these films - which appear to have been made in the 50's and early 60's - continue to show on Egyptian channels throughout the Middle East telling me there is a market for something more than channels showing Q'uran lessons and al Jazeera.
The way the upper class in Cairo speaks is, to Arabic, as the way high-end Brits speak English. I don't speak Arabic but when I was in the region a lot, I could tell if someone was from Egypt.
Where was I? Oh, yes, Atatürk (whose name translates, as you have already guessed, to "Father of the Turks"). As recently as 2008 the U.K. Guardian reported
"One of Turkey's most senior army commanders has warned the Islamist-rooted government that it will face a powerful military backlash if it seeks to alter the country's secular system."
While it appears that Turkish prime minister, Recep Tayyip Erdogan may be gaining an upper hand in moving the nation toward Sharia law, it is not likely he will risk an open fight with the military.