I'm flying first class with Delta in a few weeks. I enjoy priority security at the NY airport, first to board and disembark, priority luggage at luggage claims, extra space, large leather seats, free booze, meal, entertainment and private bathroom so you don't have to wait on a long line..If you get a good deal on the airfare its worth it but if cost 3 times coach and up, I don't think its worth it.
I'm a frequent flyer with LH and it's like the others already said. "First Class" persuades something special but the Airlines have reduced the benefits more and more. Especially the US airlines are not very famous for their front seating equipment and FC on midrange is more or less like Business Class.
But if it is your first time you'll enjoy it! Sitting in front of all, getting special attention, being the first in and out and finding a little bit more of seating comfort.
And yes, you'll definitly spare time with priority check in and safety lines!
If you really want to feel a "First Class" treatment, try long haul with Emirates, Quatar or Singapur Airlines.
BTW, we booked Business/First Class with UA as well, because it's a very special trip for us ;-) .