So let's start with this debate knowing in mind both regime are minority and are undesired and in whole hated for their dictatorial and authoritarian way.
A little background of these two countries before we head off debating;
Ethiopia
ETHIOPIAN REGIME KILLS 25 PEACEFUL PROTESTERS AND ARREST 1,500 CIVILIANS

August 3, 2013 - Ethiopian government forces open fire on unarmed demonstrators throughout the country, killing 25 and injuring dozens more, according to Ethiopian activists who took part in the demonstrations.
One witness says at least one child was among the the dead. He also stated government security forces arrested over 1,500 protesters on Friday.
For over a year, Ethiopian Muslims have been holding peaceful protests and mosque sit-ins over the regime's human rights abuses against their community and interference in their religion.
http://ireport.cnn.com/docs/DOC-1015286
Ethiopia | Big anti-government Protest to be held on the religious day of Eid al-Fitr
ADDIS ABABA, Ethiopia (AP) — Anti-government Muslims in Ethiopia on Monday called for mass demonstrations to be held on the religious day of Eid al-Fitr later this week to protest the arrests of 28 people on terror charges

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Egypt
General Sisi pushing Egypt into civil war: Analyst Graham and McCain Visit Egypt and Urge Negotiations, Not Civil War

Egypt's military chief General Abdel-Fattah al-Sisi’s wrong policies are likely to trigger “civil war” in the North African country, an analyst wrote in a column for Press TV.
Finian Cunningham said the general’s inflammatory tone in dealing with supporters of the deposed president Mohamed Morsi “is tantamount to pushing Egypt - the Arab region’s most populous country - into a civil war.”
Cunningham stated.Egypt’s military strongman General Al Sisi is playing with fire that may engulf the North African country with even more internecine bloodshed,
Tension has intensified in Egypt since General al-Sisi announced on July 3 that Morsi was no longer in office. He also suspended the constitution and dissolved the parliament.
NB; so now that you know the summarized background of these two countries, let's us begin with an healthy insightful debate of the two perspective counties and of whom is likely to fall first as an regime!!!