If your internet goes down, your baby monitor goes down. A wifi baby monitor uses your home's internet connection to communicate to servers, then to your app. So if your internet connection goes down, then you will no longer be able to stream video of your baby. That's a huge consideration to keep in mind because you never know when your internet will slow down or simply stop working for several minutes or hours, and you will be stuck without a working baby monitor. There are a few wifi baby monitors that will still communicate locally (within your home's network) when the internet goes down, such as the Lollipop or Nanit. They do this by switching from internet to local area network when an outage is detected, so you can have confidence that if you're connected to your home wifi you'll still see your baby.
It really depends on what you feel most comfortable with. There are audio monitors that allow you to listen to any noise coming from the nursery, vital monitors that track sleep and breathing and video monitors that add sight to sound. Babylist parents overwhelmingly choose video monitors. The security of seeing what your child is up to—like if they’ve gotten tangled in their swaddle, pulled their diaper off or climbed out of the crib—can be worth the extra cost of a video monitor.