Or, uhm, no.
This probably to do with Shuai jiao being more traditional than judo.
Originally Judo didn't have much groundwork either. Rolling on the ground in the battlefield was a stupid thing to do so most jujitu didn't roll on the ground much. This doesn't mean they didn't have any ground work technqique. It did have number of Lock take-down and so on which was useful in the battle. But groundwork was considered as *quickie* thing so they didn't *roll* on the ground. Obviously, this will change if it become street fight.
Judo introduced it after realising that they get busted in "contest' if they don't improve this aspect. I'm not that so sure but I read it somewhere that one school of jujitu took advantage of jujitu contest rule where you weren't allowed to kick or stamp the guy on the ground. So they just immediately lie down on the ground which is bullshit tacticis which worked if the other school had no ground work training.
However, once newaza was introduced, they discovered that superior ability on the ground is significant advantage and soon, judo start to become groundwork contest so Kodokan took delivererate step to restrict newaza to keep judo as standup arts. The old rule is preserved in number of university judo clubs as Kosen judo.
As of which art is better, I would go with "it's practioner that matter not the style" thingy. But since judo being an olympic sport, I think it has edge over Shuai Chiao in term of athlets.
Engrish does not mine strong point