Two faces of Europe's refugee debate squared off this week in Dresden, where the German antimigrant movement Pegida was celebrating its first year in existence.

Tens of thousands of supporters of Pegida, which demands immigration reforms and rails against the purported "Islamization of the West," rallied under chilly skies in the group's birthplace on October 19. Many held German national or regional banners, and others depicted pro-immigration Chancellor Angela Merkel in what might best be described as "Euro-Nazi" garb.​

Their ranks had swelled considerably from some of their poorest showings of the past 12 months, when scarcely 2,000 people had come out to stir public fears of a demographic avalanche from Syria and beyond.

They were opposed by some 14,000 counterdemonstrators. Many were championing Merkel's open-door pronouncements on accepting war refugees. Some were protesting a vicious knife attack less than a week earlier on the newly elected mayor of Cologne, who had very publicly worked to help find shelter for migrants arriving in her city.

The proceedings, marked by scuffles that left one person hospitalized, provide a window on choices confronting the continent as waves of migrants stream to Europe in numbers not seen for decades.

And antimigrant right-wing parties are increasingly well-positioned to frame the debate.

The current crisis, which has seen tens of thousands of asylum seekers and other migrants arrive in Germany weekly since September, appears to be rapidly revitalizing the political right.

The same trend is visible in other parts of Europe, where hundreds of thousands of refugees have landed or simply traversed in an effort to escape hardship only to find similarly increased support for xenophobic parties and mounting hostility to newcomers.

In some cases, those gains by nationalists and right-wing parties have been borne out by elections. This month saw the anti-immigration Swiss People's Party win nearly 30 percent of the vote in parliamentary elections on October 18 dominated by debate of migration issues. Austria's Freedom Party, which has campaigned on an "anti-immigration" and "anti-Islamization" platform for years, won over 30 percent of the vote in both October's mayoral race in Vienna and September's regional elections in Upper Austria, the country's industrial heartland.

Political analysts say right-wing parties with antimigrant agendas are tapping into fears among voters that their societies are changing too rapidly and risk losing their traditional national identities.

"Right-wing political parties try to benefit from the migration issue, as they try to benefit from fears when it comes to Islam in Europe," says Ralf Melzer, an expert on right-wing extremism at the Friedrich-Ebert Foundation in Berlin. "Both are the major subjects for their attempts to gain voters and to increase their influence."

He calls concern over migration part of a larger sense of disorientation some voters feel as Europe has been wracked by crises in recent years, including over the euro, slow economic growth, and an outflow of jobs due to globalization. Many believe their countries have lost sovereignty to the EU and now must pay the price for decisions made far from home -- whether in Brussels or in the capitals of other EU member states.

Coming In From The Fringes

Many of the rising right-wing parties started life as small groupings on the fringes of their countries' political life. But as they do well at the polls, they are increasingly moving into the mainstream and challenging their countries' center-left establishments.​

Denmark got a center-right government in June after the anti-immigrant, anti-EU Danish People's Party surged to second place in general elections. Since coming to power, the new government has taken out advertisements in the Lebanese press warning refugees not to come.

In Finland, the Euroskeptic, anti-immigration Finns Party slipped slightly in its share of the vote, but that showing was sufficient to propel it from third place nationally into second place. Meanwhile, antimigrant parties currently lead national opinion polls in both Sweden and the Netherlands.

Some political observers call the rise of right-wing parties a reaction to an absence of broader debate. Many European states have falling birthrates and their economies arguably need more workers, for instance, but migration raises politically volatile questions about whether Europeans will live in the same kind of societies tomorrow as they do today.

"What we are really seeing in the rise of nationalist parties is the combination of very significant events happening and the failure of the established political class to rise to the occasion, among other things by having a comprehensive strategy that acknowledges the scale of this issue," observes Douglas Murray, associate editor at Spectator magazine in London.

WATCH: Germany's Anti-Islam Pegida Movement Rallies Thousands On First Anniversary

He argues that ruling center and center-right parties have too often simply tried to shut dissenting voices out by branding them racist or xenophobic. But he warns that such an approach risks creating greater problems in the future.

"If you wanted to create a perfect storm in Europe, it would be this way: Bring in hundreds of thousands of people from totally different cultures, force them upon the people of Europe, and simultaneously spend your time trying to stop legitimate public discussion and discontent towards that," says Murray. "That is the perfect storm, because if people in Europe cannot express their dissatisfaction with it and see results from that dissatisfaction, then anything can happen."

The current migrant crisis has provided many examples of just how volatile things already are.

Chancellor Merkel's declaration in September that her country would welcome all Syrian refugees was seen by many in Europe as a praiseworthy gesture of solidarity with people who have lost everything to war and desperately seek a new life.

But it infuriated not only Germany's weak nationalist parties but also their much stronger counterparts in other countries. They saw Merkel as unilaterally encouraging more outsiders to try to reach the EU.

"Germany seeks not only to rule our economy, it wants to force us to accept hundreds of thousands of asylum seekers," France's National Front leader Marine Le Pen, who advocates limits on immigration, thundered at a rally on September 6. Le Pen frequently accuses Berlin, whose strong economy needs more workers, of trying to shape EU policy to serve its own interests.

The reaction in Hungary, where the right-wing Fidesz party has held power since 2010, was still more dramatic. Prime Minister Viktor Orban termed the influx of migrants a "German problem" and imposed his own solutions, defying Brussels' goal of creating a more unified Europe by building fences to seal off Hungary's borders, first with Serbia and then with Croatia, a fellow EU member state although it is outside the passport-free Schengen Area. He also challenged center-left notions of an increasingly diverse Europe by arguing he is defending European Christianity against a Muslim influx.

And amid the political sparring, there has also been rising violence. German police said this month they have recorded almost 500 attacks in Germany on homes for asylum seekers so far this year, three times the number in 2014.

The growing strength of right-wing parties for which migration is an urgent issue may now speed what appears to be a much needed political debate in Europe over where migrants fit into its future.

The debate could be heated because there are extreme voices on both sides. But it also could reveal that positions may not be as far apart as they might appear. Moderate parties on both sides tend to favor immigration that brings Europe the skilled workers it needs for future economic growth. The contentious issue is mass migration, which is difficult to control and, as the current crisis illustrates, sparks passionately opposing views of how to respond.

The EU's border guard service Frontex reported on October 13 that more than 710,000 migrants crossed the union's external borders in the first nine months of this year. That compares with 282,000 recorded in all of last year.

However, Frontex added that number may be inflated because "a large number of the people who were counted when they arrived in Greece were again counted when entering the EU for the second time through Hungary or Croatia."