Well, Watchmen began conception in 1985, when Alan Moore began developing the premise.  However, he had already been doing similar work, in the UK, in Warrior (V for Vendetta and Marvelman) as well as 2000 AD and Marvel UK (Captain Britain).  So, it's safe to say Squadron Supreme had minimal influence on Moore; rather, they were working on similar lines.  The idea of superheroes actually trying to change things for the better wasn't that unique, as both companies had already dabbled in that, particularly at the end of the 60s and the dawn of the 70s, during the "relevancy" period.  You can go farther back than that, with the social crusading of the early Superman stories, for one example.  Also, many things that Moore did had been suggested in parodies in early Mad, as well as satirical novels, like Robert Mayer's Superfolks


The difference is in the execution and the influence upon further works.  Moore was definitely an iconoclast and someone who liked to shock and surprise and pushed further than the average.  Gruenwald was a fan who found an in to professional comics via fanzines; but, never quite wanted to break the toys, just play his own games.  Moore wanted to reconfigure and even break the toys.  

One of the reasons why Watchmen became iconic and Squadron Supreme became more of a discovered item lies in the environments at the two companies, in the period.  At DC, Jenette Kahn had won the battle against entrenched old guard editors, who were churning out mediocre stuff.  She encouraged editors to think beyond what had been done, mainly because they had nothing to lose. Sales had improved in the latter third of the 70s and she benefitted in an influx of talent from Marvel, from people who were having issues with management there.  She also hired some fresh minds from outside, like Karen Berger, who then went looking for talent beyond normal sources.  The work of people like Alan Moore and other regulars of 2000 AD caught their attention and they recruited them, particularly Moore.  These guys came with that same punk spirit that infused 2000AD.  Comics fans took notice and DC marketed it.  They also sought attention beyond the normal fan press, which helped elevate their line and shine a massive spotlight on it.  That, in turn inspired others to follow in the same footsteps.

By contrast, Shooter's Marvel was spending more time improving the average of the company, without necessarily creating the new wave.  Shooter focused on creating the same experience across the line, which served to elevate the lower tier and mid-tier titles, while maintaining momentum on the upper-tier titles.  However, it didn't necessarily create the same breakout hits.  Frank Miller's Daredevil had been the exception; but, Miller had moved on to DC, by this point, though he would stop back in, from time to time.  Miller was another guys who wanted to fling some toys around.  Others, like Simonson were tweaking old favorites, emphasizing the things they always liked, and adding a new twist.  Byrne had been doing that on the FF, before defecting.  Gruenwald did a bit of that, but never quite as forcefully as a Gerber or Engelhart.  He seemed to have more of a reverence for things and seemed to want to work within the world established, rather than shake it up.  However, Squadron Supreme does move a bit outside that box.  Thing is, it is a logical extension of what Engelhart did with the group in Avengers and DeMatteis did in Defenders.  Gruenwald just took it to the next step.  Now, there are elements that were edgier than the norm at Marvel, such as the brainwashing of Lady Lark, by Golden Arrow; but, they had precedents in other Marvel books.  Still, despite pushing further than most books, Squadron Supreme fell under most radars.  It did respectable, but not spectacular. The difference is that Marvel treated it as just another Marvel title, while DC treated things like Swamp Thing and Watchmen as big deals.  That did more to influence others.

Squadron Supreme seems to have been discovered by more fans after the fact; particularly in the wake of Kingdom Come and Mark Gruenwald's death and the trade release, with his ashes mixed in.  Gruenwald literally had to die for Marvel to realize what they had there.  In my opinion, Squadron Supreme's impact didn't really begin to appear until the New Millennium, as the increased attention brought it to new fans.  Watchmen had an immediate impact and a lasting one.

Personally, I think if Gruenwald had conceived Squadron Supreme at DC, or Marvel of the earlier 70s, then he might have been encouraged to go even further than he did.  It is a good series and there is a craft there.  I don't think Marvel's printing quality helps it, as the art is a bit muddy in some issues.  Also, Paul Ryan wasn't that developed as an artist, yet, compared to others.  I tend to wonder what it could have been, with someone like Paul Smith involved, let alone someone more experienced, like Simonson.  Gruenwald and Perez would have really been an interesting pairing on that material.