Private vs Public Health Insurance - Interesting question

While for the public scheme insurance more or less everything is fixed by law (and thus the difference between insurers negligible), the private scheme offers hundreds of tariffs with different coverage, advantages and disadvantages. They can also exclude or surcharge for pre-existing conditions.
You really have to read the fineprint - or get an independent adviser to evaluate it for you (Note: Those who live off insurer's commissions and thus do it without fee for you are NOT independent!).
Also note that once in the private scheme, it is difficult or impossible to switch back. The costs are expected to rise much slower in the public scheme - and once you have dependents (non-earning spouse or kids), who are covered free of charge in the public scheme but not in the private, it usually becomes unattractive to switch (or then you'd regret to have switched).

One also has to verify they are allowed to get private insurance. There is a minimum income to even join, or if one is a civil-servant (Beamter). Many foreigners assume everyone can get private insurance if they wish but it is restricted. And while there are some exceptional scenarios, usually a public option is better by far.

What is also available to anyone is private supplemental insurance. One still has the public option but the supplemental will pay for things not covered like a private room in a hospital or some non-recognized therapies. The cost vary widely depending on what it covers. This would usually be the best approach if one wants more perks.

Thank you for the answer.

Yes I am aware and I am eligible for a private insurance.

However, my point was:  is there a premium "PLAN" which covers exactly same things that public insurance covers ?

If there is, then I would be saving ~100eur by switching from public to private.

Private insurers sell themselves as better than the public scheme, and almost all plans do offer more coverage (to justify the higher price). Their highest "premium" plans, which can cost thousands of Euro per month, are geared towards the super-rich and cover single room in the best hospitals, transport there by helicopter, etc., etc.
But there is also, by law, a "Basistarif", which every insurer has to offer (but since it's loss-making, they do not advertise it and will do anything they can to dissuade you from taking it). It offers basically the same coverage as the public scheme, at a similar price. (There are only few differences: For one, you cannot cover non-earning family members for free, and on the other hand they have more possibilities to throw you out or restrict coverage in case you don't pay the fees.)
The "Basistarif" was meant for pivately insured people who become destitute and need government assistance. In that case the authorities must also pay those people' health insurance - and because switching back to the public scheme is basically impossible, the lawmakers created this basic tariff to prevent unduly high costs for the public purse.

To get an overview of the (hundreds of available) tariffs of private insurers and evaluate the advantages and disadvantages for your situation, you better consult an independent insurance adviser (for a fee - the "free" ones live off insurer's commissions and are thus not independent!).
Also keep in mind that, once in private, you cannot switch back when the fees grow much faster (with age and deteriorating health) than in the public scheme (as is generally expected) or if you acquire a family and suddenly have to pay a multiple (as dependents are not covered for free).