The key difference between the two was also the most obvious: geography. Japan's isolation (and Egypt's lack thereof) played a significant factor in its rise to prominence. I don't have the requisite expertise (and thus sources on-hand) to speak to the other dimensions in Japan's rise, but I can address your main thesis.

Egypt in the 18th and 19th centuries, despite holding political autonomy, was in fact under the suzerainty of the Ottoman Empire. A restored Mamluk order controlled Egypt for most of the 18th century, paying nominal tribute to the sultan but exercising vast amounts of domestic control. The French invasion of Egypt at the end of the 18th century quickly defeated the Egyptian forces, and remained in control of the country until driven out by a combined British-Ottoman force in 1801. The French occupation served as a dramatic catalyst for much reorganization of Egyptian society, and that would be taken further by a soldier of the Ottoman forces.

Muhammad Ali was an ethnic Albanian who was raised in Greece, who came to Egypt as part of the Ottoman re-occupation force. He quickly rose in the power vacuum of post-France Egypt and was recognized as governor of Egypt by the Ottoman Sultan in 1805. Recognizing the need to reorganize Egyptian society in order to compete in a rapidly-blossoming capitalistic society, he implemented extensive reforms to Egypt's education system, military, agriculture, and in particular industry. It was this drive for industrialization that ultimately spurred Muhammad Ali to conquest, and in turn brought Egypt into the larger web of diplomacy that served as the backdrop for 19th century global affairs.

After having previously added the Hedjaz region of Arabia (with the Sultan's approval after quashing a revolt there) and parts of Sudan (without the Sultan's approval) to the Egyptian domain, Muhammad Ali decided to turn against the Ottomans after the disastrous experience suffered while aiding the sultan in the Greek War of Independence. In 1831 Muhammad Ali invaded the Levant, quickly extending into modern-day Syria and Lebanon. This provoked the Ottomans to seek European help, and Russia responded by signing the defensive Treaty of Unkiar Skelessi. This prompted a crisis in Britain, whose primary goal was to maintain the balance of power among the major European states (and in so doing, minimize the influence of other Great Powers in the Ottoman Empire.) Together with France, the three European powers intervened and forced an end to the war. However, Egypt was allowed to keep its conquests under the administration of Muhammad Ali's son, Ibrahim, who had commanded the conquest.

Ibrahim did not prove to be as capable of a governor as he was a general, though. The Syrians rebelled against the heavy-handed nature of his attempts to implement his father's reforms, and the Ottomans soon took advantage of these revolts to launch a campaign to recapture the lost territory. Ottoman forces were routed at the Battle of Nezib, however, and soon the Egyptian army was in a position to potentially push on to Istanbul itself. This, of course, was absolutely incompatible with Britain's aforementioned goals, and the expansionist dreams of Muhammad Ali were quickly brought to an end by a British-Ottoman expedition that forced Ibrahim to retreat back to Egypt.

The Treaty of London (1841) forced Muhammad Ali to relinquish all his conquests (with the exception of the Sudan) and imposed restrictions on Egypt's military, but did allow for the governorship of Egypt to become hereditary. This treaty, in combination with the Treaty of Balta Liman that had been imposed on the Ottomans and their territories (including Egypt), brought about a significant decline in Egypt's financial, industrial, and military potential.

It was in these circumstances, then, that Isma'il Pasha came to rule. The Egyptian cotton boom of the 1860s (made possible by the lack of American cotton available during the Civil War) and Isma'il's desire to modernize brought rise to the second great period of Egyptian reforms. While these reforms, particularly in education and infrastructure, were successful in bringing Egypt closer to the European models, they were also expensive and brought Egypt into vast sums of debt. The European powers (in particular the British) were able to use this debt and their influence with the Sultan to ultimately have Isma'il deposed in favor of his son Tawfiq.

The disposition of Isma'il and the preferential treatment of foreign creditors that Tawfiq was forced to agree to soon became sources of discontent for the Egyptian populace. A relatively minor incident in the Egyptian army soon gave rise to a movement centered on Colonel Ahmad Urabi, who was peasant-born and able to rally huge support from the army and the lower classes. His popularity led to his appointment as Minister of War, and led the Khedive Tawfiq to rely on foreign support to keep his throne. The British and the French, fearing a nationalist Egypt that could cut off their access to the Suez Canal, supported the more-pliable Tawfiq and soon a British expedition was authorized. The British forces landed near the canal and defeated Urabi's forces at the Battle of Tel al-Kabir, bringing an end to his movement. The British, who had originally intended a simple incursion to support the khedive, would ultimately remain in the country until their expulsion in 1956.

In conclusion, Egypt's primary limiting factor in the 19th century was its position in geopolitics. While situated on the periphery, Egypt was very much a factor in the balance of power that had been constructed in the wake of the realignment of post-Napoleonic Europe. Upon upsetting this balance, the European powers used their positions of relative strength to impose upon Egypt restrictions that hindered their ability to successfully continue industrializing. Without the ability to overcome an economy based on agricultural export, Egypt was thus unable to invest in modernization without bringing severe liabilities upon itself. And with these instruments of debt and firepower, Britain (and the wider European establishment) was able to establish hegemony over Egypt for the next half-century.

Sources:

Cleveland, William L., and Martin Bunton. A History of the Modern Middle East. 5th ed. Boulder, Co: Westview Press, 2013.

Goldschmidt Jr., Arthur, with Aomar Boum. A Concise History of the Middle East. 11th ed. Boulder, Co: Westview Press, 2016.