Which of the Bitcoin wallets between the Online and Offline works best?
There is no unambiguous answer to this question, but from my point of view, a purse is better at the exchange.
The matter is that they are very reliably protected. Plus you do not need to store a huge purse on your computer.
Another disadvantage of the purse on the local machine is that if the computer breaks down, access is problematic and the accumulated funds are considered lost. Especially if the purse was lying on a disk with the operating system.
Also it is worth considering that bitcoin transactions are rather slow. If the growth or decline of a certain currency has started, you will not be able to respond quickly from the local wallet.