The two men can be seen together all over central Cairo, on banners, flags and on posters on sale to tourists and locals. One is moustachioed, square-jawed, handsome, with short greying hair and an enigmatic smile; the other is clean-shaven, open-faced, most often in dress uniform, a clutch of medals on his left breast.

The first man is the pan-Arab nationalist former Egyptian president Gamal Abdel Nasser, hammer of the Muslim Brotherhood, who died in 1970. The second is General Abdel Fatah al-Sisi, head of Egypt's armed forces and, since the July coup that ousted the Brotherhood-backed president, Mohamed Morsi, the supreme power in the country.

In the coffee shops of Cairo, where political discussions have bounced off peeling walls since Nasser's death, a vigorous debate is taking place over whether Sisi has deliberately risen in the former's likeness – and what parallels between the two men's careers may mean for post-revolutionary Egypt.

While Sisi has pledged stability as a central plank of the military-led government he will shepherd towards elections in nine months' time, he has also tapped into themes that Nasser used to enshrine his legacy as one of modern Egypt's most celebrated figures.

"Despite 40 years of painting a bad portrait of Abdel Nasser, whenever there are bad times, people always conjure up his image," said a Nasserist activist and leader of a political bloc that champions his tenure. "Sisi has not got the same hold on the Egyptian consciousness. Not yet."

In his public appearances since the 3 July coup, Sisi has mirrored Nasser's key messages of nationalism, scepticism of western intentions, Arab dignity and strong leadership. The latter has been seized on by a broad swath of the Egyptian public that has struggled in the chaos of the revolution that brought down Hosni Mubarak's presidency in January 2011.

"There is a craving for a strong leader," said a western diplomat of Sisi's popularity. "Nasser is still revered here, although I don't think he deserves it. I'm not sure he did much good for the country. There is this misguided belief that only a strongman can sort out the mess that is Egypt."

While Nasser was credited in the Middle East as a figure who did much for Arab unity, he was also criticised at home and abroad for leading through a cult of personality and for doing little to develop civil institutions, or advance human rights.

The parallels between him and Sisi run deep. Nasser had a background as an officer and became president with military support in 1956, after planning the revolution that had ousted Egypt's last monarch, King Farouk, four years earlier. Sisi also has a revolution under his belt. And, while not currently an elected official, he is being talked about as a presidential candidate after the interim government ends.

"Nostalgia for Gamal Abdel Nasser is the result of the Egyptian people's awareness that the army has embraced the people's wishes and made sure that the revolution could take place," said Hamdeen Sabahi, a presidential candidate in 2012 for a bloc of Nasserist parties, called the Popular Current. "Here the Sisi phenomenon is introduced. He has become very popular since 3 July.

"The question remains, to what degree can the new system of government fulfil the needs of the people, especially their social and economic needs, and to what degree will he be able to hold on to his image as a saviour.

"We have to make a distinction between Sisi as a person and the military institution he represents. He has a good chance to prove himself now and there is a sense that he represents the Egyptian national identity that the Brotherhood wanted to steal away."

Amr Moussa, Arab League head and former Egyptian foreign minister, said the groundswell of support for Sisi, right, drew a distinction between the stances taken by Nasser and his legacy, which for many remains chequered. "It is not a call for a return to [Nasser], rather one for nationalistic stands and attitudes," he said. "The armed forces embrace these stands and they are personified through Sisi. For this reason, is not so much a yearning for a Nasserite movement, it is more a sense of nationalism and support for the military.

"We are all yearning to return to democracy and to have elections as soon as we can. I don't think that the army forces and its chief are interested in playing politics. Six to nine months of transition to approving the constitution and civilian rule will be the order of the day."

Even among Sisi supporters there are those who doubt that he or the military will extricate themselves from playing a decisive role in civil affairs after new presidential and parliamentary polls and a mooted constitutional referendum.

The deadly showdown with the Brotherhood, which remains bitterly disenfranchised and encamped in two parts of Cairo shows no sign of being conciliated. Sisi's generals have repeatedly warned during the past week that both sites, at Raba al-Adawiya and near Cairo University, will be cleared imminently. Planning is underway to turn that warning into effect after the Eid al-Fitr festival, marking the end of Ramadan. More bloodshed would likely cast a pall over a legacy that remains very much in the making. Although some Egyptians feel that another showdown – two massacres have already taken place since 3 July – may be a price worth paying, despite almost certain condemnation from some western states.

"The thing that links the two is that Sisi, like Nasser rejects the west and wants national independence," said Mohammed Fahim. Both men fighting the Muslim Brotherhood is not seen as a bad thing."

At Nasser's shrine, not far from the Raba al-Adawiya sit in, bouquets of dried and cracked flowers sit alongside the sand-swept marble tomb of him and his wife. Sentry boxes outside stand battered and abandoned; the guards who once paid homage here were cut under Morsi's rule as part of a so-called efficiency drive.

Nasser, the man the Brotherhood wanted to forget is, however, very much part of the new Egyptian psyche. "It's up to Sisi whether he leads by example, or just reflects in his glory," said Fahim.

Additional reporting: Marwa Awad

• This article was amended on 8 August 2013 to clarify the status of Eid al-Fitr.