America has the largest economy of the world (and Greece does not). While that is only a soft fact, it is an important soft fact. America is the world's only country which can print the currency in which it has its foreign debt (Greece obviously cannot). While that is unfair to the foreign holders of that debt, it is a great advantage for Americans. And, finally, America is an excellent place for foreign investment (and Greece is not). If foreigners no longer want to hold American debt instruments, they can invest the money in, for instance, buying all the S&P companies; half of Manhattan; perhaps all of Florida; etc. Now to the similarities.
Compared to 30-40 years ago, America has become radically de-industrialized. Goods which used to be manufactured in America are now being imported. An American quote from the 1970s: "If the Japanese want to work 18 hours a day in exchange for us signing promissory notes, that's fine with me". Well, it's no longer fine because the manufacturing jobs went to other countries as well. Greece never had that much manufacturing but much of the little that there ever was is now gone. Why? Because Greeks preferred signing promissory notes to other countries for imports instead of manufacturing themselves.
It is not a conscious decision to "sign promissory notes in exchange for other people's manufacturing". It just happens. It happens when other people's manufacturing becomes cheaper than one's own and when one has the creditworthiness to issue promissory notes at low interest rates.
When countries import more than they export, they incur a trade deficit. That trade deficit becomes a current account deficit when other incomes from abroad (like tourism) do not fill the gap left by the trade deficit.
A country's current account deficit represents the transfer of wealth from it to the rest of the world. The American current account deficit peaked around 7% of GNP; the Greek one was twice as high at its peak.
Free international trade is always cited as a major factor in creating wealth of nations because it leverages on the efficiencies of the division of labor. That is correct as long as international trade is more or less balanced over time. If international trade becomes structurally unbalanced, the following happens.
Some countries import the products they need (and lose jobs) and other countries manufacture and export them (and create jobs). The exporters generate cash from abroad which they have to lend to the importers so that those can continue to pay for imports. The consumption-addicted and no-fear-of-debt-minded American consumer became the importer; the hard-working Chinese with low labor costs became the exporter. America was drained of cash and China built it up. That way, the American consumer has been for decades now the major locomotive of world-wide economic growth. The price he paid for that was indebtedness. The price the Chinese paid was having to make loans to Americans.
The Greek consumer also discovered that it is more fun to let other people work and pay for their work/products with promissory notes. Thanks to the Euro, Greece assumed the same creditworthiness as, say, Germany and could borrow cheap money like there was no tomorrow. Germany accumulated cash which it had to lend, and it lent it to Greece. That way, Greece became a mini-locomotive for the creation of wealth in Germany.
The American mantra of the last decade has been: "We sell each other houses at inflated prices with money borrowed abroad" (and the real estate bubble built up). The Greek mantra was: "We sell each other souvlaki at inflated prices with money borrowed abroad" (and the whole country became a bubble).
"It takes two to tango!" International trade requires two parties who can benefit one another in order to create wealth for both. Remember the "opium war" of the 19th century. The British were crazy about tea from China and they imported it. The Chinese insisted on being paid in silver. The British scraped up every silver they could find and gave it to China as payment for tea. Instead of using that silver for buying, say, manufacturings from Britain, the Chinese refused to trade and sat on their silver. Britain ran out of silver and China accumulated it. Since the British did not want to stop drinking Chinese tea, they had to find other ways to get some of the silver back from China. They discovered that the Chinese loved opium as much as the British loved tea. So the British smuggled opium into China, received payment for it in silver so that they could use that silver to buy tea from China. And that lead to war.
America has been "ripped off by China" for decades now the same way that Greece was ripped off by, say, Germany since the Euro. However, the "ripping-off" needs to be clarified. If one people prefers high consumption with little work and another people prefers high work with little consumption, the "ripping-off" is a voluntary meeting of mutual interests. That system, however, can only work as long as the cash-receiving people are willing to lend that cash to the cash-paying people.
A country's Balance of Payments must balance. This is an issue of mathematics and not economics: never can more cash leave a country than enters the country in the first place. It may leave the country as wealth and it may return to it as debt but the accounts must balance!
Greeks may argue that a country like, say, Germany "owes" Greece to provide financing because Germany took profits on Greece by being able to export so much over the years. That is principally not false. However, the German profits were made by private sector exporters while the financing is provided by tax payers. Of course, from the Greek standpoint it is "German cash" but from the German standpoint it does matter from which pocket the cash comes.
If international trade does not become structurally more balanced, the world will become more separated into the "have's" and "have-not's". The "have's" will have many jobs and lots of cash, and the "have-not's" will have diminishing jobs and lots of need for cash. Germany and China will be among the "have's" and America and Greece will be among the "have-not's". Given the positive soft facts surrounding the American economy, it will continue to attract other people's cash for much, much longer than Greece. Given the negative soft facts surrounding the Greek economy, the voluntary inflow of cash has already stopped.
Americans and Greeks can congratulate themselves for having contributed to the creation of jobs and wealth elsewhere. The price they paid for that is indebtedness to people elsewhere.
The only long-term solution to these problems is to seek ways how international trade can become structurally more balanced so that wealth creation becomes structurally more balanced.