London (CNN Business) Two of Europe's most popular online banks are making a big push into the United States. But they may struggle to win over consumers.

Berlin-based N26 and its UK rival Monzo have signed up millions of young professionals in Europe by offering free accounts that can be opened in minutes via smartphones.

Consumers have readily adopted the companies' apps, which are packed with innovative features that traditional banks don't offer. They don't charge fees, and they make budgeting easier.

Yet they face intense competition in the United States from established banks and tech giants that are trying to muscle into the sector. Experts say the European upstarts will need to improve their game to impress Americans.

Big in Europe

Monzo, which has 2 million customers and is adding another 200,000 a month, is known for its flashy coral debit cards and focus on customer service. N26 boasts 3.5 million users and a slick German app design.

Both banks offer powerful budgeting tools. Their apps allow customers to budget and track spending by splitting cash into different buckets within the same account.

They give customers free ATM withdrawals, and make the account opening process painless: customers can sign up in the app itself and then verify their identities via video.

It's these functions that the banks say will give them an edge in the United States.

Chase JPM Bank of America BAC Both are also partnering with US banks, meaning Monzo and N26 customers will enjoy the same deposit insurance as accounts with established players likeand

Yet European customers can also attest to drawbacks. Even in the digital age, brick and mortar branches come in handy. And many consumers prefer speaking to a human when taking out loans such as a mortgage.

N26 in particular has stumbled. The bank does not offer customer support over the telephone, instead directing users to a chat portal within the app.

It has also been ordered by the German government to improve its ability to prevent money laundering and terrorist financing (the bank says it has taken measures to prevent financial crime).

When the bank addressed the government order on Twitter, N26 users flooded the company's tweet with customer service complaints, including from people who were struggling to access their funds.

Growing pains

Still, N26 says it continues to grow apace with 10,000 new users signing up each day. It's valued at $3.5 billion, and has been backed by Hong Kong billionaire Li Ka-shing and PayPal co-founder Peter Thiel

Monzo is meanwhile valued at nearly $1.3 billion, according to CB Insights, and is partially backed by American investors, among them Joshua Kushner of Thrive Capital.

Both banks are loss making, though they have different plans for breaking even.

Monzo says US clients could eventually be able to switch energy and other utility providers from within its app in under a minute. The commission it collects on such sales allows it to offer UK checking accounts for free.

"Customers can switch to a cheaper provider simply and with little effort," Tristan Thomas, head of marketing and community at Monzo, told CNN Business.

"We imagine doing the same across all services and features," including investments and loyalty programs, he added, comparing the strategy to operating a kind of app store for services.

N26, for its part, plans to offer faster paycheck processing and bank cards made of metal. In Europe, N26 charges a monthly fee for the boutique card and users pay for premium accounts that come with travel insurance.

Tech challenge

Critics say the startup European banks remind them of American online-only banks that sprang up and then disappeared during the dot-com boom.

"My view is it's going to be like the late 90s," Joseph Dickerson, an analyst with Jefferies Equity Research, told CNN Business. "This is just a repeat of the last movie."

Dickerson said that online banks lack the same level of engagement as lenders that that offer telephone and branch customer service. And younger customers demand more from a bank as they age.

Over half of millennial customers prefer face-to-face interactions for big financial decisions, Dickerson said, "and this is where these banks fall short."

An even greater risk to Monzo and N26 could be competition from established peer-to-peer payment services like Venmo. Google and Facebook have also made moves into payments.

Thomas, the Monzo executive, said the London startup can still carve out a niche for itself in the United States. Not by emulating legacy players, but by "offering the best checking account experience in the world, and then offering the best deals in the market via our marketplace," he added.