Tired, hungry, weak from the heat, they speak of a harrowing journey -- and the joy of finally making it to Germany.

But in Budapest, the scene is more desperate.

On Wednesday, refugees in the Hungarian capital held up scraps of paper: "Help Syrian," they read. "Babies are tired."

Still, almost anything -- even this -- is better than the chaos and killing from which they have fled: in Syria, where cities lie in rubble; in South Sudan, ravaged by war and poverty; in Libya, where warlords maraud and people suffer; in Iraq, where ISIS likes to video its slaughter of innocents.

These lands are no place for families to thrive. No place to raise one's children.

In Budapest, the migrants -- free at last of bombing and war -- lie listlessly, waiting to board trains for Western Europe.

But they are denied by authorities. Hundreds wait. Still, they have experienced much worse than this.

Wildly varied response

Europe is in the midst of a migrant crisis. The response of various European governments has varied wildly.

On Thursday, Hungary's Prime Minister Viktor Orban plans to meet with other members of the European Union to figure out how to cope with the emergency. His nation is a transit point for migrants trying to make their way north. And Hungary has responded by erecting a fence along its border with Serbia.

In Germany, the interior minister will address parliament, after a planned asylum center was burned down.

Germany's government has been more accepting of asylum seekers, but political leaders there have had to contend with xenophobic protests.

On Tuesday, police arrested a suspect in an attack earlier in the week on about 40 asylum seekers in a shelter in Brandenburg.

And in France, migrants shut down the Eurostar cross-channel service between England and France overnight as they poured onto the tracks near Calais, the French entry to the channel tunnel. Trains between London and Paris and London and Brussels were turned back.

Caught in the middle are the desperate men and women, with children in tow, who have fled wars in Syria and Iraq in overcrowded, sometimes deadly voyages by land or by sea.

In just the latest example, at least 12 people traveling on boats filled with refugees drowned off the coast of Turkey, Turkish officials said Wednesday, according to the country's semiofficial news agency, Anadolu.

The incident took place after two boats left Bodrum, Turkey, and were trying to reach the Greek coast, Anadolu reported.

Passports and visas, please

At Keleti station in Budapest on Wednesday, tensions simmered.

Hundreds of people who had expected to board trains to head on to Austria and Germany found Hungarian police officers barring their way.

They want to make their way to Western Europe, where they hope to claim asylum.

The journey for almost all of them has been arduous.

"We have been here five days. No food, no sleep -- no place to sleep, no anything," one Syrian refugee at Keleti station told CNN on Tuesday.

He and other travelers had train tickets but were not being allowed through, he said.

"The problem is the amount of migrants with the wrong papers," said Reka Hegedus, a spokeswoman for the train station. "Obviously, even if they have tickets, it is not enough."

Only those with proper documentation -- a valid passport, a ticket and any necessary visas -- were being allowed into the station, with police checking the papers of those seeking to enter.

"European regulations require that a person wishing to go on to Austria or Germany, for example, has the necessary documents," a government statement said. "People at Budapest's Keleti railway station demanding to be allowed free passage are demanding something which is not possible under European legislation."

Flashpoint: Hungary

Hungary has come under increasing pressure from Western European countries to change its approach to the migrant crisis.

It has been erecting a barbed wire fence along its more than 100-mile border with Serbia in a bid to prevent migrants crossing illegally as they make their way north.

Hungarian government spokesman Zoltan Kovacs told CNN's "The World Right Now" the lack of documentation was a key issue for authorities.

"That's one major problem we have to face: that these people at least to the Hungarian border came without papers, or got rid of papers, and at the end of the day it's basically impossible to determine whether they are telling the truth that they are coming from Syria or other war zones," he said.

In an earlier statement, Kovacs called on Germany to clarify its position on allowing Syrian refugees into Germany from Hungary, "calling for order and legality to be restored at the borders of the European Union."

Strangers in their own country -- now in Serbia

Refugees flood into Germany

Even with the bottleneck in Hungary, migrants were still making their way to Germany, just not many by train.

Germany's government said last month it expected up to 800,000 asylum seekers to come this year -- four times more than in 2014.

At Munich's main station, though, the arrival of refugees slowed to a trickle because of the restrictions in Budapest.

"It was so hard for us. It took a very long time," said a woman from Afghanistan. "Especially in Hungary, it was very difficult to get through Hungary. We had almost no food and water."

German Chancellor Angela Merkel said Monday that her country -- where some are opposed to taking in asylum seekers -- must show "flexibility" when it comes to dealing with the crisis.

European Union member states agreed in July to take in more than 32,000 migrants to ease the burden on Italy and Greece, where the largest numbers have arrived. Another 8,000 should be allocated by the end of the year, said the European Union's commissioner for migration.

Things to know about Europe's migrant crisis

Varying sentiments

For the most part, the German public supports Merkel.

Local football clubs hoisted welcome banners over the weekend. Villages held "refugee welcome" parties for the newcomers. And a recent news poll estimated that 60% back Merkel's warm welcome.

Some other countries are just as welcoming.

In Reykjavik, Icelanders called on the government to accept more refugees from Syria.

Others are reluctant.

One of them is Slovakia, which said last month that it only wanted to take in Christians because it has only a tiny Muslim community and it would be hard for new Muslim arrivals to integrate.

The foreign ministers of Germany, France and Britain issued a statement Friday asking a special EU council to meet later this month to work on measures to better manage the influx of migrants.

How you can help in the migrant crisis

See the latest from CNN teams in the field

CNN's Archith Seshadri, Arwa Damon, Gul Tuysuz, Frederik Pleitgen, Antonia Mortensen, Alexander Felton, Carol Jordan and Bharati Naik contributed to this report.