I've done both those plays (in fact, I've both performed and directed
different productions of each).

The biggest problem (for us) in each production of Birdie were all the
sets...this play has a different set every five minutes. We did rent the
plans from Scenographics for one production, and they helped a lot. The
music is fairly easy (as long as you have good electric guitar and electric
bass players) - the vocals aren't that tough. There's lots of dancing - but
mostly fun (and relatively easy) contemporary/modern dancing (no ballet,
tap, etc.). Costumes are fun and easy.

"The Boyfriend" is adorable. But many MANY young people (and even
some of their parents) won't get what's funny about it. It's a parody of a
style of theatre that is completely unknown to contemporary audiences.
The songs are fun - a couple of serious voices required - and there is
dancing, Dancing, DANCING. Lots of tap-dancing and 'real' dancing
required. Costumes are fun - more involved than Birdie costumes - and
many can be rented. The final scene masquerade ball gives lots of
costuming opportunities for a good costumer. There are only three sets -
one set for each act - so it makes sets a breeze. I just saw the Goodspeed
Opera production of The Boyfriend this summer (directed by Julie
Andrews, who played Polly in the original Broadway production) and it
was nothing short of an absolute total delight.

Both are really charming plays - very very different styles.