ok, I´m playing often a good ZSS with my DK, and we have always epic close matches.
I´m gonna write in DK´s view.
Strengths:
Power. range. priority. Seriously, if we hit you with a punsh, fsmash or usmash @ 80, you´re dead. dsmash @ 100 uspmash and 9punch, you die @ 60. actually it should not happen that often that we hit with fsmash, but usmash ( against downB) and punsh is good.
range. we have one of the best melee ranges in the game, and ftilt can cancel out your b and sideb.
if we hit with all hits of a grounded upB you get 36 %, which is in that case, your half stock.
bair is a move you should watch out for, bc we can do 2 in one sh, with suprisingly good range ( it can go through your downb as well).
When your on theedge, you´re screwed. I know every little option you have. you ledge attack sucks and get eysily outanged by ftilt. downB gets wrecked by bair or usmash (death). stand up and shield will get you ftilted and your back on the edge.
edge guarding can be a risky. we can gimp you with bair, spike you with fair or dair, but you can spike us ith downB, too. so it´s all about spacing.
we´re fat *****. we live usually to 150%. that´s a problem for you, bc you die at 80.
Weaknesses:
A good ZSS has a amazing stage control with sideB, neutral b. we´re obviously a big target. who of you didn´t get a 50-70 % string on a fattie? really, you can combo as to hell, uair usmash upB all string together nicely. you could thinkthat´s a huge problem for us, but if you think about how long we live and how long you live, yeah.
your armor part´s are diffcult to get around, but if you´re not careful we can use them against you pretty well (ever seen a glide toss by DK? 1/4 fd length).
ZSS can limit our options pretty well, but we´re lucky that we have such amazing bair.
If it goes to killing, you can kill us @ 150 if your sideB is fresh, bair can work and downB(difficult to hit).
If you´re in the air, you can have aproblem bc dk can juggle and punish you well, your dair or downB can work, but also can be punished.
I would say it´s a good 50:50 match, but it´s also stage dependant.
you want to try, to limit DK´s options with sideB and neutral b, and we will go for an aerial approach with bair, maybe you can punish that. we´re should not approach on the ground, bc you can grab us out of the sheild easily if you fire a neutralB.
if DK is inside, you will have a problem. don´t cp jungle japes, brinstar, delfino or yoshis island against DK.