Laurel and Hardy…Except This Time, Hardy Is Comatose
What can you say about these two that hasn't already been said?
They're one of the great duos in all of cinema—the tall, thin guy and his short, fat buddy predate them by quite a bit, but they found their own rhythm early on and show no signs of stopping here.
In any case, unless you've been in a coma for the last 40 years, you know these guys.
C-3PO is a fussy and high-maintenance droid, prone to panicking and quite the snooty-patooty when he wants to be but also quietly affectionate to his friends. R2-D2 is much more reliable: dogged, friendly, loyal to a fault, and willing to stand up and be counted when the chips are down.
For this one, the boys are left on the sidelines for most of the film. C-3PO remains steadfastly beside Princess Leia, acting as her butler/interpreter/ex-husband annoyer:
C-3PO: Goodness! Han Solo! It is I, C-3PO! You probably don't recognize me because of the red arm. Look who it is! Did you see who? Oh. Excuse me, Prin—uh, General. Sorry.
That's basically his thing here, and he doesn't deviate from it. Show up, bug Han, deliver some key plot exposition, and hang out with Leia until the credits roll.
R2 is a little more interesting on that front, which is weird since he pretty much doesn't move for 90 percent of the film. He fell silent after Luke left and basically exists as a giant paperweight when we first see him here. Credit C-3PO for being really bummed about it:
C-3PO: R2-D2 has been in low power mode ever since Master Luke went away. Sadly, he may never be his old self again.
This is definitely in keeping with what we know about R2: he loves his buddies so much that he might just shut down out of sheer electronic grief when Luke goes into exile.
Turns out, he's kind of playing possum on that front…which plays into his loyalty, too. When Luke left, he knew he had to leave behind a way to reach him again, but he didn't want the bad guys finding out first. Who are you going to trust with that information? The astromech droid, that's who.
R2 is even willing to go into semi-permanent power-saver mode to make sure that happens, coming back to life only when the right people have the right info to induce him to spill the beans..
And for all his fussiness, C-3PO understands that. You can't trust Goldenrod the way you can R2, but underneath that type-A, butler thing, C-3PO really cares. You see that when R2 finally wakes up, confirming that these two really are inseparable:
C-3PO: Oh, my dear friend. How I've missed you.
Gets us right in the feels, every time.