Woody.

I don't think somebody as dumb as Woody could actually survive in modern urban America.

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One too many fast balls because Coach was practically insane. He should have been in an institution! No way he could survive on his own!

Woody. Even if he wasn't dumber, he was annoying. I liked Coach.
RIP
Paul Gray
1972-2010

Too close to call.

Neither is dumb, so much as taking almost everything literally.

Woody was a great replacement, but Coach, as "dumb" as he was, did have a reason to be slow as the OP points out, but he also had a very strange depth to him. He knew how to manipulate, and every once in a while an anger would rise from his character being that he was a coach in the past (when he coached the kid's team is a great example, featuring Corey Feldman When he tells the one kid, "Go home and tell your mother you're a flop!" is one of the funniest lines ever).
So I think Woody is smarter on a surface level as in, he's younger, more normal, more innocent and sweet and not stupid in that sense. His sweetness keeps him from being a quick-witted person. But Coach was a deeper character, and those layers come through the more you watch the show. It's like the person he was in the past would rise up every once in a while, and then he'd lose it again.
Woody was great, but Coach, during the first two seasons, was my favorite And yet CHEERS is an off-shoot of TAXI, and both Coach and Woody are basically sober characters based on Christopher Lloyd's Jim, with a little of Tony Danza's punchy boxer thrown in.
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Was Yogi dumb?

I love Nintendo. Still my favorite console.
Movies in theater: Indiana Jones and the Last Crusade 10/10. Vacation 8/10. Psycho 10/10

I doubt I was the only one who thought Woody was a younger version of Coach. Was Coach inspired by the late Yogi Berra?

Yeah you're right they were low on book smarts but they were good with people. Everyone seemed to like them. I really loved both of their characters.
Equal love for everyone.

Toe-ma-toe/Toe-mah-toe
po-ta-to/po-tah-toe
Six of one/Half a dozen of another
NEITHER EVER had book smarts! BUT BOTH had people skills
HOWEVER Coach certainly had his years of hits to the head, Alzheimer's ect. working against him whereas Woody was simply naive or perhaps a little slow IMHO
I fell asleep during INCEPTION BUT I FEEL like I still saw it!

Coach.

Tough question. Woody's lack of smarts seems born of being naive. The question may be unanswerable.

Coach had brain damage from taking too many fast balls to the head. Woody seems to be just born dumb.

Probably Coach. Woody at least knew his own name.

Coach.
Woody might not be city witty, but he is certainly sharp.
When Sam begged Woody back to tend, Woody wanted a $100/mo raise Sam tried to change the subject, to which Woody tricked Sam back into 'only having to give him $30 a week raise instead'.