This is a very interesting question. Married with Children and Malcolm in the Middle are absolutely my favorite two TV shows. They're similar in the fact they both defied what "the typical American family" was like with exaggerated disfunction. Married with Children wanted to be the anti-Cosby show and it definitely accomplished that. Married with Children helped pave the way for shows like Malcolm in the Middle. I do think that Married with Children was more popular and had a larger impact on pop culture only because it was one of the first shows of its kind and it ran for 11 seasons. What made both of these shows work through was that at the end of the day you knew these families cared immensely for each other.
MARRIED WITH CHILDREN, without a doubt, was more popular and had a bigger impact on pop culture than MITM.
I believe, along with THE SIMPSONS, MARRIED was one of Fox's first TV shows and the audience was broader. It set the tone of the Fox network. The writing on MARRIED may have been lowbrow, but it's funny how MARRIED was criticized then, when its humor was really similar to THE SIMPSONS.
I think MITM's humor was more in the post-FREAKS/GEEKS era. Who knows how it would have evolved if it had gone on for a few more seasons!
Married with Children was definitely more popular for a simple reason that if you think back there were less tv channels and total number of tv shows back then. Today people flip through their 300 channels or go online. The culture is far more fractured. So a lot more people saw Married with Children and it was a much bigger part of the culture.
Comparing the two now, Married has a lot of funny jokes and sentiments and like Malcolm has interesting characters. But Married is painfully awful in terms of any type of cinematic quality or the dreadful laugh track or the terrible attempted physical comedy. Remember Malcolm was essentially shot with movie technology and style where as comedies from 90's and before where pretty much fixed sets and fixed cameras with a stage and audience. It is pretty awful stylistically and technically.
There definitely is a common theme among the two shows. This is of the common, downtrodden family who no matter what problems they have themselves, always end up seeing it as them against the world and stick together. No matter how dysfunctional you want to call these characters or what awful things they get themselves into, there is always that nugget at the core of family unity and loyalty and that they will stand up for themselves and each other.