Going to dissect Karta's list here, with some more accurate comparisons between 4.4 and 6
>>Ability to join Wi-Fi networks and control paired Bluetooth devices from quick settings
Joining wifi networks and controlling bluetooth has never been a problem...ever. If you want an easier button to access them from, you can download millions of them from the store.
>>Official support for multiple SIM cards
vs the unofficial support that worked in 4.4. Not that it is going to matter to you in your case.
>>Device protection: if a device is lost or stolen it will remain locked until the owner signs into their Google account, even if the device is reset to factory settings.
I have first hand experience now in that there is no way into a device without the devices logon password, and that it has no problem deleting your shiat when you mess up. Oh and no amount of access from the google account connected to it will save this. If you don't know your phone password, your fsck'd. That said, the whole "after the wipe, you can't unlock the phone without the account credentials" thing is..bogus, currently. Even the security patch from days ago can be circumvented with a little thumb action (The problem is the phone lets you stray too far into its programs while locked, eventually allowing you into an app that can link accounts to the phone).
>>Native WiFi calling support
vs all the wifi calling we have been doing on 4.4 so far. Even with google voice.
>>Introduction of Doze mode, which reduces CPU speed while the screen is off in order to save battery life
Sounds promising on paper, probably works to an extent, but prepare for notification delays on apps you expect instant notifications from. This just needs time to perfect. Apple has been doing this since the S5 days. Growing pains. Ignoring doze how ever, the monitoring and control of the power used by apps is much stricter and in the hands of the OS, not the app, making for a much easier time in preventing rogue apps from draining your phone suddenly.
>>Application search bar and favorites
more stuff you delete from your home pages.
>>App permissions now granted individually at run-time, not all-or-nothing at install time.
Much better app control for the paranoid. Ontop of this, you get much less restricted use from memory cards. 4.x pretty much has the sd card locked down to media only, and apps could not edit this stuff unless it created it in the first place. I was so annoyed at not being able to delete songs from my music collection.
>>Security updates
for as long as samsung updates your phone, and how frequent. This isn't new among carriers and no winners here I am afraid.
The rule of thumb still comes down to, do you need more then what your phone offers? more power? a better camera? a better screen? Your S3 is pretty ancient, a current flagship completely outclasses it in every way. Your new OS would be the least of your changes.