A classic case of precedence:
Rock crushes scissors.
Scissors cuts paper.
Paper cover rock.
Not a classic case of precedence:
What to do? Follow me.
Deal Breaker: Weddings.
Weddings trump shower, as active participation rather than mailable gifts is the reason for your presence. Also, weddings are the perfect excuse. Those who invited you to the bridal shower would unquestionably prefer that you attend their wedding than someone else’s bridal shower; presumably those pregnant have the same fond hope and/or recollection of their own nuptials.
Now the point of contention – the showers. Baby shower beats bridal shower. This is when external factors come into play: when your invitation was received, with whom you share more friends, which might miss your presence, who will need you to create the illusion of a large and vibrant crowd. Most importantly, which is more fun.
Rule of thumb: baby showers are fun, and filled with people who don’t know a thing about child care. These are people who need your help. Once they and their friends have had a few kids, the parties tapper off – in the meanwhile enjoy the goofy gifts from others and make sure the first-time mom has a starter kit of diapers and pacifiers.
Alternatively, there is a solution which involves no thought at all – close the blinds, lock the door, and stay home.