The problem with this question is that it is highly speculative and subjective. Crosby's work on the Columbian Exchange and Ecological Imperialism argue that the rise of Europe was due to a biological and environmental advantage. Europeans had horses and some immune resistance to contagious diseases, and therefore were better able to conquer the Americas.

While biological explanations work (to some extent) for the Americas, what about Africa? The first thing to note is that Europeans could not colonize Africa until the 19th century (excluding Portugal and Angola, which was a unique case - see Miller, Way of Death). This is well known in historical circles, but I find that in teaching, students are blown away by the idea that Europeans simply could not colonize Afrifca in the 16th, 17th or 18th centuries. Walter Rodney, one of the absolute best historians and activists working in the 1960s, wrote in 1967 that it was well known that Europeans operated on the coast of Africa only because the local rulers permitted them to trade (Rodney, West Africa and the Atlantic Slave-Trade). The best reasons for the lack of European dominance are threefold:

1. Europeans died or deserted their posts at incredibly high rates. Davies, Royal African Company has some statistics, and he provides some anecdotal evidence in his North Atlantic World (pp. 84-85) suggesting European mortality rates as high as 50% within a year.

2. The ruling Africans in all the areas along the coast from north of Angola to the Senegal river were powerful rulers, who exerted a strong sense of control over their territories. It is true that they did not see land ownership the same way as the Europeans, but the idea that someone under their protection could just be seized off by Europeans in high enough numbers to satiate the New World's desire for labor is just obsurd. Rodney provides this evidence: "After being surprised on a few occasions, the Africans on the coast naturally kept watch for their European attackers and defended themselves vigorously," (Rodney, West Africa, p. 5). The number of Europeans that they could physically transport to Western Africa paled in comparison to the number of resident militarily trained Africans.

3. What did happen was that Europeans were able to build up capital, gunpowder weapons, and a standing army trained with modern weaponry that allowed them to gain a foothold in Africa. From there, the various European "colonizers" would play politics. There were constant internal divisions or wars going on in various places in Africa, the same as had existed in Native North America, or Europe for most of the early modern period, and so the Europeans would play one side against the other, while being sure that both sides were provided the military armaments to attack each other. And with several centuries of slave trading destroying the demography of West Africa, the Europeans had a leg up.

The same is true of India during colonization. England used local elites and access to trade good to manipulate themselves into power. One of the forgotten elements of colonization is that it was not purely at the expense of the locals. Colonization was achieved at the the expense of most of the locals, while an elite or select few made substantial gains in wealth and power.

To sum up: Almost any historian today would say that nothing in history is inevitable. The smallest events or happenstances can dramatically affect centuries of history. What if tobacco as a commodity never caught on in England, as James I hated the stuff and found it foul. What if certain strains of disease persisted in Native America, causing epidemics among all the Europeans? What if the Armada took England, Africans became unwilling to trade with Europeans, or if the native Indians (meaning India) refused to assist colonizers? Any one of these events could have gone either way. So was European conquest inevitable? No.

But did Europeans have biological, financial, and military advantages over the territories they attempted to conquer? Yes.