What's missing in this discussion...
... is the fact that your personal details are far more vulnerable in others' keeping than your own. I've been pwned four times to my knowledge. Adobe, Linux Mint, LinkedIn and vBulletin have all exposed varying amounts of my personal data because of their poor security. Troy Hunt's Have I been pwned is worth being subscribed to.
Cross platform password keeper I use is Password Safe. It works with Windows, Linux, and Android. It's popular and FOSS so likely as secure as can be.