If you install Firefox in Debian 8 from the Debian repositories, you’ll get the latest version of the ESR 45 release. Updates tend to be available in the Debian security repositories pretty much at the same time as they’re made available for auto-updates in the ESR channels used by Firefox itself; the latest release, 45.8, was uploaded to Debian and released to the Firefox update channels on March 7 2017.
In Debian 9, you’ll get the latest ESR, whichever that is (Firefox is one of the packages where major version bumps are allowed into the stable release); as of early 2019, that’s 60.3, with 60.5 coming soon.
If you install Firefox from Mozilla, you’ll probably get the latest non-ESR release instead. You can also get this as a Debian package from the Debian testing and unstable repositories, as the
If you’re the only user on your system, I’m not sure there are many pros or cons. One big advantage of using a package to install your browser is that it can then satisfy the various dependencies from other parts of the system (e.g. your desktop environment). If you stick to the “stable” packages, you’ll get security support without any habit-changing updates; whether that’s a pro or a con depends on what you’re looking for. Other than that, security-wise both approaches are similar (for single user systems, again); note in particular that the Debian Firefox packages are maintained by a Mozilla employee (both in the main repositories and in the Debian Mozilla repositories).