As always, there's a problem with defining "best," because typically people think of it as "favorite," which might not necessarily be the "best" in filmmaking terms -- which is itself a subjective determination, I know, but hopefully folks know what I mean about a difference between which one you prefer versus the one you think is superior in sheer quality. Sometimes they are one and the same thing, but other times they might not be.
My favorite film of the series is "Empire Strikes Back" for all of the reasons Tom Harris mentions, plus the fact that it has the greatest light saber duel of the series, it has the greatest line of the series (from Vader, and you know which one it is), it has the second-greatest line of the series (Han: "I know"), it has the best moments depicting Yoda ("That... is why you fail") in the series, it has the best Vader uniform of the series, it has that fabulous chase through the asteroid field that is the best space chase sequence of the series, it may be the only film of the series with true twists and shocks (the door opening at Cloud City to reveal Vader at the table, Leia shouting out to Han that she loves him, Luke fighting fake-Vader in the cave on Dagobah only to see his own face under the mask, Vader revealing that he's Luke's father), it introduces Boba Fett, and it has the most buy-in to the characters of any film in the series (meaning it's the best distillation of every individual character and the actors are really going all-in to portray their emotions and personalities).
There is an epic feel to this film's moments and themes that gives it an air of classic legend, and it's helped along that path by a musical score that is probably the best of the series as well.
On the other hand, it does also have some extremely cheesy dialogue in many places, it doesn't make sense that Luke's entire training to become a Jedi (and remember, after this training, he is a Jedi, because he returns to Yoda in the next film and is told he's learned everything he needs already) takes about a day or two, since he flies through space to Dagobah, crashes and meets Yoda, and does all of his training in the same time it took the others to have their chase through the asteroid field, get to cloud city, change clothing, and go to lunch (with that surprise guest). Yoda ends up wise and dignified, but he starts out like Grover from the Muppet Show shouting "Mine! Mine!" for a shiny penlight.
And like all of the first three films in the series, it is a tale about a galactic empire fighting an interplanetary rebellion, yet there are two planets in the entire film and only a handful of ships, and each film never takes on the true size and scope that the prequels could attain due to the advances in filmmaking technology and special effects. Say what you will of it, but "Attack of the Clones" had a final battle that looked like an interplanetary civil war had started, and "Revenge of the Sith" was a galactic space opera of epic proportions that looked like an Empire versus the start of a rebellion.
The latter film there -- "Revenge of the Sith" -- is the other contender for "best of" in my opinion. While "Empire" holds a special place as my favorite and is a neck-and-neck contender for first place, I think "RotS" is pound for pound the strongest space-fantasy epic etc etc etc of the entire series. There's no denying the scope of this film, that it feels like an adventure spanning a galaxy, that there are powerful character arcs that include major changes in the lives, personalities, and worldviews of all major characters, and it's a really terrific story full of tragedy and drama and destiny. And as an adventure, the action and ships and aliens and battles and effects are spectacular to behold, and the score of this film rivals "Empire" as well. It is a huge, smashing successful end to the trilogy and to the story encompassed in the six films, which gives this one added gravitas.
There is, quite honestly, not much that I can find to criticize about this film, and the biggest complaint I hear about it is that, compared to the cast of the original three films, the actors in the latter trilogy don't have the same magical chemistry. To that I always feel I have to say, most films actually lack that magical chemistry, but that's because they reached a special place in that ensemble that few films really do achieve. Lacking that same degree of chemistry doesn't mean the others failed, because that's an extremely high standard and in truth "RotS" has very fine acting from very solid actors, and it's just by comparison to that rare example of the gold standard in ensembles that these criticism can even be leveled.
I think we also have to accept that for a lot of us, our extra-special feelings for the original series and insistence that it was nearly flawless etc stem at least in some tiny measure from the fact many of us were kids when we first saw it, and quite frankly there'd never been anything like it before. It was magical and breathtaking and new. The later trilogy suffered from the fact that technology had caught up, viewers were used to seeing such magic, and the original films had that aura of unattainability. If we are perfectly honest with ourselves, I think we have to admit that there is in many ways as much cheesiness and... let's say "less than ideal" dialogue in "Return of the Jedi" as there was in any of the prequel films, and there was plenty of goofy jokes and kid stuff (Ewoks, anyone?) in that film as well. But again, it was that magical place of ensemble acting and characters we'd come to love so much for their newness and originality and how different the whole thing was. Anything else was bound to seem like a pale reflection after that, wasn't it?
Even if, rather than being a pale reflection, it was actually among the finest sci-fi/fantasy films ever made, a great space adventure with an operatic climax that closed out probably the darkest, most serious, and -- I will go ahead and say it -- best written film of the entire series. "Revenge of the Sith."
So I have to call it a tie. And sure, that's a cop-out, but this is Star Wars and in that magical series, we can have TWO "bests"!
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