That's a great question! Our popular opinions about these groups—good and bad—are deeply impacted by histories of nationalism. Nationalist attitudes continue to impact our opinions today, but I'll do my best to stay within the 20-year rule and focus on the deeper roots of these attitudes.

In terms of stereotypes, conquistadors have often been seen as having been Spaniards abroad, as opportunists or adventurers who established a vast empire that eventually fell apart. In a sense, nobody owns their memory since they have no enduring legacy. Vikings, in contrast, are typically seen as the ancestors of modern Scandinavian countries as well as the first Germanic settlers of the Americas. Nationalists on both sides of the Atlantic proudly point to these ancestors as a confirmation that today's political order rests on ancient traditions.

Both of these stories are myths. The conquistadors were racially mixed, and the Spaniards among them were often acting outside the political structures of Spanish authority. Our idea of "Spanish" conquistadors actually relies on an overly simplified version of the past and in some ways even obscures what actually happened. The Vikings are similarly a modern invention that obscures similar diversity. Did the settlers of Greenland really have anything in common with the skull-crackers of Lindisfarne, other than—perhaps—a shared tongue?

Who benefits from these stories? Well, lots of folks. The conquistadors have been depicted as evil Spaniards since as early as the 1500s. Spanish missionaries laid some of the groundwork for this in their efforts to assert the humanity of Indian peoples, claiming that conquistadors had unjustly dehumanized them and were denying them access to the Christian faith. European competitors latched on to this narrative to curate the Black Legend of Spanish depravity, which helped justify their own efforts to establish empires in the Americas. During the Age of Revolutions (which were complex!), some Latin-American revolutionaries similarly pointed to the early colonial past to paint the Spanish as unfit to rule, leading to a revival of indigenous nationalist identities. That is to say, there have been (and perhaps continue to be) lots of nationalist reasons for portraying the conquistadors as unjust oppressors.

Similarly, the pro-Viking myth sustains a variety of nationalist narratives today. Modern Scandinavian nationalists look back to the Viking Age as the time when their countries were first unified as kingdoms. Seemingly peripheral communities in the North Atlantic see the Viking Age as a time when they could see themselves as being at the center of a globalizing community. Icelanders pride themselves on speaking the most direct descendant language of Viking-Age Norse. And in the US, the Vinland sagas have provided a rebuttal to the story that a Mediterranean Catholic (i.e. Columbus) first discovered America, which was a useful counter-narrative for 19th-century US Protestants. Scandinavian immigrants to the US subsequently pointed to this same story to justify their immigration in the face of Nativist discrimination. In short, there have been (and perhaps continue to be) numerous nationalist reasons for portraying Vikings as noble explorers and settlers.

There's other important factors behind why our opinions of these groups diverge, with gender and race being two of the most salient. Popular images of Vikings skew hyper-masculine, and these images have been co-opted by white supremacists for generations. These are important problems in their own right, and I've written specifically about the importance of women's contributions to the Viking Age in a recent AMA thread. However, I don't think these issues have direct parallels in how we think about conquistadors (or at least these issues fall outside my expertise), and so I won't pursue them here.