Actually there are alot of similar more so then that when comparing KSS to Smash.
First of all unlike most of the Dream Land Series and Kirby's Adventures (Understand I never played the 64 game) Special Abilities in KSS could do many different attacks with combations of different controls. The Cutter Ability is has been quite common across all the games. In KSS you could throw the cutter or Tap attack over to do the final cutter when you were near an enemy. When you hit attack while dashing would do a swing of the cutter, and pushing down in the air and attack you'd drop down with the cutter at an angle (Which looks oddly like Sonic's Dair in Brawl). Though there are obiviously more combations in Smash then in KSS it was a similar concept.
Another concept in KSS, the helper concept which would allow Kirby to give up his ability to summon a parnter which could be controlled by the 2nd player which was also fairly similar to the way SSE co-op works. But more then that, in KSS most helpers couldn't do the flying like Kirby does so to make it across gaps, they could perform a continual jump that moved much like Kirby's flight. Though it was restricted to one for most characters in Smash, for alot of characters it looks quite similar to that thought train.
KSS by most I've met has been considered the Highlight of the entire Kirby series. It's not really all that surprising that Sakarai made it similar, it was a formula that produced positive results and it looks like it works for the type of game it is.