We also got both and this was our experience. The swing was a Graco Open Top and it was great for soothing the baby. Mine went into a trance and didn't make a peep for an hour or more. I have heard about others finding it the only solution to calm a colicky baby. He started liking the swing at about 2 months old.
The bouncer was a Fisher Price Rainforest Bouncer which is now the Precious Planet Bouncer. And this is by far the best baby thing we got. There are lots of types of bouncers and some look great but aren't bouncy or aren't comfortable. This one is perfect and I have not found another bouncer that is as great!
My baby is now nine months and long ago learned how to bounce himself and can spend an hour or so just sitting in the bouncer and looking around.
I have several friends who have fancier bouncers but their babies likemine the best.
I would think you should KEEP both gifts depending on what kind of swing and bouncer they are. Exchange them if you think the model/brand isn't something your kid will love.
If you need to take one of them back, I say keep your bouncer if it is colorful and bouncy and will accommodate your child's growth for at least six months.
My baby stopped really caring for the swing but I think most babies love swings. And when you are busy with dinner or taking a shower, it is nice to have options for how to keep your baby occupied.
Feel free to email me if you'd like to know what kinds of swings my other friends have gotten and hated or loved.
Congratulations on having a baby! They are the best!