I think some of the disagreement here is that the term "greatest" is a subjective term. For some fans, it means most impactful. For others, it may mean most memorable, or the one with the greatest story behind it. And, for others, it may mean the play with the greatest degree of difficulty to pull off.
Yes, the Stolen Base will remain one of the most talked about plays in Boston sports history. But there were a whole bunch of plays that had to happen before and after that play to make that play have the significance it did.
So, I can see why people would vote for any of the Field Goals. Even the 23 yarder in OT in the Snow Bowl probably deserves some mention, as the weather and field conditions were certainly not getting any better by the time overtime rolled along.
My own personal thoughts: While I was amazed when Vinatieri's kick actually went through, at the time it seemed more of a reprieve. They still had a long way to go, and I was under no illusion that they would beat either the Steelers or the unstoppable Rams. But when the clock went to 0:00 in the Super Bowl with Adam's kick sailing through the uprights, I was absolutely stunned. I was like: did I just see the Patriots, aka the very definition of a laughing stock clown circus since their founding, just win a freaking Super Bowl? No, that can't be right. The field goal had a certain bit of a Bobby Orr moment to it, even if it was far less exciting (Lonnie Paxton's snow angel doesn't come close to Orr sailing through the air).
But, having said all that, the Butler INT checks a lot more boxes. Most impactful to game outcome by far, completely unexpected, almost infinitesimal probability (that's a play that is 99.99% of the time a catch or incompletion; usually goal line INT's happen when the QB forces something into traffic near the middle of the end zone), amazing execution and preparation, an improbable series of plays leading up to it (Kearse catch, followed by Hightower's tackle), and some compelling back stories to boot (rookie UDFA that most Pats fans never even heard of before the play; Pats win one after a couple of disappointments; Brady cementing his reputation as the GOAT despite Collinsworth's faux outrage during the game commentary about ball deflation).
So, yeah, it's the INT. But I'm OK with anyone voting for the Field Goals.