I have to hand it to you guys who've been using T-Mo's Galaxy Tab 3 - you've been powering through with Jelly Bean (4.2, no less) for...ever. Looks like all your patience is finally paying off, as T-Mo is now sending KitKat to Tab 3s over the air.
That's the only change T-Mo is noting in its changelog, but let's be honest here - do you really need anything else? Nah. Android 4.4 in itself will be a fairly significant improving on the aging tablet.
Head into Settings > About device > Software updates to grab it.