The Galaxy S III, first released back in 2012, only has official software support up to Android 4.3. No matter: the folks at the CyanogenMod development team are keeping the device alive long after Samsung threw in the towel. Today the AT&T, T-Mobile, and Sprint variants of the GSIII all get their very first nightly ROM builds for CyanogenMod 13, which is based on Android 6.0. You can find them at the d2att, d2tmo, and d2spr listings on the CM download page, respectively.

In contrast, Asus has already promised a Marshmallow build for the Zenfone 2, which is less than a year old at this point. Even so, if you're not willing to wait then you can grab the nightly build of CM13. It's listed under Z00A for the 1080p version and Z008 for the 720p version (these may not be live yet, but should be very soon, hopefully in the next nightly cycle). CyanogenMod 13 is also available for the Zenfone 2 Laser and Selfie variants. Also getting the CM13 treatment is the original NVIDIA SHIELD Portable, the one with the controller and clamshell screen combo. It's listed under "roth" (may also not be live yet, but going live soon).

You'll need to have a custom recovery to flash these ROMs - TWRP is available for all devices. As with all nightly builds, beware of a few bugs, and wait for the more stable builds if you need something reliable for a daily driver. Grab the Marshmallow version of Gapps to flash alongside the ROMs if you need access to the Play Store and other Google services.

Source: CM download page