I asked this exact question to a friend a couple days ago. Here's the answer I got.
Ok, so here's what's different on the 777 vs the K3:
Front end -
Longer upper arms, curved and braced to be stronger/stiffer
3 hole C-Hub mounting for adjustable upper arm length
New bushing based adjustablility for the A/B blocks, with both High/Low starting points.
Narrower servo saver posts
Upside down servo saver, much easier to adjust
Center -
Lightened Center Diff/Spur Gear
Engine move forward and more towards the center
Servo tray lowered and moved inward
Rear -
Narrower inner hingepin mounts
Longer arms without making the truck wider, ends are turned up to allow longer shocks w/o too much downtravel.
4mm longer shocks.
Overall differences - Thicker shock towers, less of the brittle titanium screws, parts are countersunk which avoids a pile of those little countersunk washers, which reduces weight.
Now, the differences between the standard 777 and the SP 1 -
Shocks are completely different (no teflon pistons and no hardcoated shock bodies)
Most of the aluminum isn't the nice blue stuff, the shock towers are thinner.
No universals
No lightened center diff/spur
Different clutch
Different engine mounts
No TCD front diff
The differences between the 777 and the SP1 are a bit different than the differences between the MBX-5 and the ProSpec. The MBX-5 is already a pro quality kit and the ProSpec is a hopped up kit. In contrast, the 777 SP1 is a pro quality kit and the standard 777 is not nearly pro quality kit that the SP1 is.
Overall, the 777 SP1 was instantly faster for me. It steers better, it recovers from being out of shape easier, it's lighter, transfers weight better and responds to smaller setup changes. If you don't already have one, I would suggest the 777 SP1. As far as necessary hop ups, I think a set of CNC front knuckles and CNC chassis braces are all that are "necessary". Knuckles are expensive and you can pick up like 5 sets of stockers for the price of most CNC ones, so you can always just get stockers and swap them every once in a while before they fail.
Hope this helps!