A few prominent reasons come to mind, but the most common thread is far more incentive, and next to that greater relative economic power over the non-white population. It’s true that population shares were similar: at their peak, European settlers amounted to 15% of the Algerian population. At their peak, white South Africans amounted to 22% of the South African population (in the early-mid 20th century), but for most of the history of Apartheid proper, this was significantly less.

1. Europeans in Algeria had more of an option to just leave. Algeria was politically part of France, so that the white people in Algeria were French citizens. It was also much closer to Metropolitan France. Moving back there was not at all as much of an ask compared to white South Africans, who were nearly all citizens of only South Africa.

2. White South Africa had a deeper history and thus identity, infrastructure, culture of its own. Algeria was settled by the French after the 1830s. A slight majority of white South Africans (and the overwhelming majority of the Apartheid-era government) were Afrikaners who had had a presence there since the 17th century and had a new identity, while Anglo-South Africans had started settling there from the early 19th century before the French took Algeria. Asking them to just move back to Europe in the mid-late 20th would be like asking the same of white Americans, except imagine times had changed by the later 1960s on to the point South Africa was a pariah state.

3. Another aspect of this is that, as with the U.S., the ‘colonial power leaving’ meant Britain giving South Africa independence. And this happened in fact earlier than it did in Algeria (with further autonomy given to the Union of South Africa in 1910 and South Africa becoming a self-governing ‘dominion’ in 1931). But it ceded power to a white government - considered not only acceptable by London but necessary and even ‘progressive’ in the early 20th century. Attitudes changed across the West by the time of the French war in Algeria.

4. France had to consider international opinion. After the economic damage of WW2, and with the Cold War threat, the France of the era of the wars in Algeria, Suez and Indochina was in no position to prioritise colonial rule over all else, and the opinions of the U.S., Europe and the international community mattered more relative to their rule of Algeria, as ‘integral’ as this was made out to be. The issue still overthrew the Fourth Republic, but it was not remotely the war of ‘national survival’ that it was felt to be by much of white South Africa, who were prepared to pay the price of decades of sanctions. But other considerations for Metropolitan France itself came first.

5. Arabs and Berbers in Algeria were more unified - they consisted of two ethnolinguistic groups with one religion, similar to other countries in the region, and had a greater level of socioeconomic development overall than black South Africans. In contrast, the black South African majority was divided into several ethnic groups (the largest of which, the Zulus, largely supported a very different party, the IFP, from the rest, who largely supported the ANC), and had a significantly lower average annual income - one proxy measure for how easily they could influence the French or equip themselves against them. Meanwhile, white South Africans were significantly richer on average than French settlers in Algeria (see: Alvaredo, Cogneau, Picketty: ‘Income Inequality under Colonial Rule, evidence from Algeria, Cameroon, Indochine and Tunisia’).

Here's the (short) answer I provided for this question some time ago. Since more can always be said, I'll add that we must take into account the global context, which is that by the early 1960s France no longer wanted to maintain its colonial Empire, for political and economic reasons. It had been through two bloody and costly decolonisation wars at this point so keeping Algeria was out of the question when nobody except the Pieds-Noirs wanted to keep it.