With the right equipment it is possible to recover the previous data from a single pass overwrite on magnetic media with a moderate degree of certainty. To do so, one needs to tap the analog signal from the read heads and look for amplitude variations due to remnant magnetisation from the previous state after the mean level of the current state (as determined by a normal digital read) has been subtracted. It needs specialised equipment and probably a clean room but can be done at a price. However, walk the flux right round the hysteresis loop and then randomise the final state and the previous data becomes unrecoverable. N.B. on drives that don't have a secure erase function, some data may remain on sectors that have been marked as failing and reallocated by the on-drive controller. Reading such sectors at the very least requires hacking the drive firmware, and may require specialised equipment and a clean room. The main barrier is the cost, and also, for those with criminal intent, contracting for such services without compromising their own identity.
Unless you have data on the drive that a three letter government agency would be interested in, or that's commercially/financially sensitive and worth over $100K, or you are a person of interest to the media, DBAN's default three pass DoD Short method is good enough for spinning rust drives or secure erase for SSDs.
Make sure you've got the key codes/numbers for any software you intend to transfer the licence of with the machine and do a full reinstall of OS and any applications, before wiping any electronic copy of the keys you may still hold on any other machine or media. Its extra hassle but if you want to maximise the resale value by selling it as a working Windows PC, (without giving away your bank codes), you don't have any other option.
Failed drives should be physically destroyed.
Drives with highly sensitive data should be physically destroyed, and unless the platter surfaces are degaussed or physically eradicated, the remains should be incinerated at a high temperature. Flash chips can simply be chiselled off and pulverised.