Here are some calculations, to show it in starker contrast...assumptions are from the reports in April about the cap going to 92M in 2016-17 and 109M in 2017-18.
Because of CBA minutiae, it's not a straight "35%" or "30%", but close. Here are the basics of what KD would make guaranteed
If KD signs a max deal this summer, a team must have $26.2M in cap space. If he signs a full, 4yr non-Bird max, he'll be guaranteed 4/$111.8M.
If he re-signs with OKC (Bird max), he'll be guaranteed 5/$150.5M. So he'd immediately be giving up 1yr and almost $39M guaranteed to come to, say, POR. But it gets waaaay more interesting than that. He's at the 9-year vet point this summer, which means he can get 30% max of the cap. If he is a UFA next summer (2017), he can make 35%. Of a cap that's projected to go up to $109M. So, let's say he signs a 1yr deal this summer with anyone, versus a 1 year keeping his Bird rights...
Team must have $35.9M in cap space in 2017 to sign him, unless it's OKC re-signing him.
His 2016-17 salary (26.2M) + a 4 year, non-Bird, (any other team) will net him 5 years, $179.3M (already $29M over what OKC just by themselves could give him this summer)
His 2016-17 salary (26.2M) + a 5-year Bird max (only OKC) gives him 6 years, $232.4M (or 2 years and $120M more guaranteed than, say, POR can offer this summer)
Now, we've seen players take less guaranteed to go where they want to go (coughTexcough) but even in the best non-OKC scenario (where he signs a 1yr max with anyone this summer and a 4year max with anyone with 35M in cap space next summer) gets him 5/$179M. By staying in OKC he could make another year and $53M more guaranteed.
Regardless, he will almost assuredly not be signing a long-term contract this summer, unless his knees are secretly on the Brandon Roy plan.
Edit: Man, I must've been drunk when I wrote this. Arithmetic errors all over the place.