Some people will say it depends on the baby but I never experienced that (not yet, anyway!). I didn't think I needed both, but received a bouncer as a gift. The swing is a MUST for me. The only times I used the bouncer were to bring my daughter into the bathroom with me while I showered and got dressed, which was definitely very useful and important! This time though, I may wait on getting a bouncer or another alternative for the same portability purpose, because the swing I'm getting (FP Zen) lets you take the seat off and it is supposedly really easy, but I haven't tried it myself yet. (BFF says she did it every day for the same take-to-bathroom-for-mama-to-shower purpose and it was easy.)
I think it also just depends on your needs, your house, etc. I would not skip the swing though, totally awesome. Travel swings are also great!