Oops! Late as usual (Planetary next).
I've seen the TOS and DS9 tribbles on several occasions, and from what I remember, The Trouble with Tribbles is one of the better episodes (I'm a big TOS fan, but there are a lot of terrible episodes - just terrible). For sure it's a tongue-in-cheek episode, which I think works well in a SF series once in a while to counterbalance the more earnest stuff, but there's also a modicom of drama with Darvin's plot, and conflict with the Klingons. My only complaint, which happens a few times across all ST, and other SF, is a member of an alien race disguising themselves as another. Just bribe some mofo guys. It's not Balance of Terror or City on the Edge of Forever, but it's great fun.
I can remember being absolutely astounded the first time I watched Tribbles and Tribble-ations. DS9 was well into it's stride, and Sisko was turning out to be a brillant commander. But still, T&T stood out for the way it combined clever use of the TOS plot, the weaving together of the two crews, and showing love for the original and its wit, all bookended by the brilliant, tone-setting Department of Temporal Investigations. I don't know whether it's possible to enjoy T&T without having seen the original, but as a Trek fan, it ticked all the boxes.
So, I just watched MT,MT. Oh dear, the episode didn't work on any level. I imagine TAS was marketed to the young end of TOS viewers and even younger animated cartoon viewers in general, so I imagine, for them, the episode would have been as dull as ditchwater. Nothing happened. I think someone had the idea that TTwT had been a successful light-hearted episode so let's do that again for the kids, but just didn't understand what made the original fun.
The few episodes of TAS I've seen so far have generally been very good, considering the format, the market and the era, and it definitely works better when it's working on original ideas: Yesteryear and Beyond the Farthest Star work really well.
Summary: tribbles knock Jar Jar Binks and Ewoks into a cocked hat