What is the most secure ECC Curve? I have for a while used Koblitz curve (sect571k1), in ECDH and ECDSA. But I have started wonder if it is the most secure. I prefer security over efficiency. So the curve doesn't have to be the most efficiency curve.

I'm not looking for a curve that is only secure today, and the next few years. The compute power increases rapidly today, and I'm looking for a curve that is secure as far as possible in the future. So if someone is able to steal my encrypted data today, they should not be able to crack it in next 20 years, hopefully longer.
There is no such thing as the most secure curve. For one you can always come up with a larger curve if you need one. For another there are many measures of security and not all curves are directly comparable.

If you wanted the curve for which the current best known attack is the slowest, then by that measure sect571k1 is actually the most secure out of the curves that are in use.

However, that is not necessarily a very useful requirement, because any curve for which the best known attack is slower than ~128-bit strength equivalent will never be broken without either advances in attacks or the arrival of practical quantum computers. Those advances need not apply equally to all curves, while quantum computers would break all curves regardless of strength.

Binary field curves like the one in question are sometimes considered more risky because better attacks are known than for prime field curves of similar size, so it is thought that new attacks are more likely. That is a judgement call.

Likewise there are other measures of security that do not apply to all curves. Perhaps the most talked about is the potential for some kind of backdoor in the parameters, which makes some distrust NIST curves in particular and any curves without a good explanation for the parameters in general. Also things like ease of secure implementation may matter in practice.