Both Lastpass and 1password browser plugins worked totally fine for me on Linux. My only complaint re: 1pass is the lack of native Linux app — you can't do mildly complicated things in the browser extension like edit credentials. On the other hand, LastPass doesn't have a native app.
LastPass doesn't have a native app because it doesn't need one -- when the browser plugin and web vault are working properly, they provide all available functionality on every platform. The problem is that the plugin does not always work properly; see my other comment about copy/paste problems on Linux, a bug which LastPass has known about for many months and not fixed.
