Broadly, constant borrowing is sustainable, just look at any European economy. As long as your tax base grows faster than your interest payments there’s no unavoidable problem.
This? It’s not sustainable. Sooner or later this will result in a correction. This could range from aggressive budgetary measures, an internal crisis all the way to China monetising its overseas investments (which are extremely extensive).
European economies are hardly poster children for constant borrowing. Most of them have been in enforced austerity for years, and have only managed to avoid much tighter spending cuts because the ECB is funding governments through vast amounts of money printing (which boils down to confiscation of savings). Result: huge government spending overruns, ever-falling savings rates.
Erm... Spain and Greece has been in enforced austerity, no other countries I can think of. And neither have had typical, responsible borrowing patterns. (Nor does Italy, but it’s dodged that bullet.)
(Ireland had some problems just after the crunch but a) entirely because they took on a bank they could have let fail and b) they’ve paid that off now.)
Portugal, the UK, Italy to some extent (though nowhere near the level they need). Europe is basically a continent of governments trying to cut their spending levels, some with more success than others.
The UK isn't in enforced austerity. Austerity is a political choice here (driven by a desire to eliminate the deficit), and a pretty bad one (the IMF said we should be spending more, also it looks like we will be irrespective of what the public wants soon because of Brexit). Basically, whilst the UK's economic woes are self-inflicted, over-borrowing isn't the cause of them. Italy definitely has over-borrowed, but its problems go way deeper than that and I wouldn't describe its spending right now as "austerity". Portugal, like Ireland, has already dug itself out of the hole.
Going back to my original point: if increasing your revenue faster than increasing your interest payments, you can do this forever. Sure, the credit crunch gave some countries a shock, but you really should read up on exactly how egregious the Greek borrowing situation was. It was insanely unsustainable. Germany, Denmark, Sweden, France, Slovenia? They'll be fine.
You can't compare the Euro countries to China because the European countries are borrowing in what, in essence, is a foreign currency. For those countries, constant increasing of the debt is hardly sustainable.
China has not that problem. The only danger for China is inflation (that can be controlled with, for instance, taxes), otherwise, the People's Bank of China can buy directly the debt and nothing would happen. In fact, they could just stop emitting debt, but that would be inconvenient for banks and other big investors.
Private and local government debts is a different issue.
This? It’s not sustainable. Sooner or later this will result in a correction. This could range from aggressive budgetary measures, an internal crisis all the way to China monetising its overseas investments (which are extremely extensive).