If you are really interested in scanning as a hobby and not just a general interest, then a handheld will serve you better than an app. All scanner apps get their audio from Broadcastify one way or another. This means that if someone takes the feed offline (or Broadcastify has a server error), then it is just down and there's not much you can do about it (mad/sad posts don't usually solve it eg.
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3). Besides what has already been noted, another pro is that the scanner can also pick up things that aren't generally provided online as a feed or on an app (per policy), and there is a lot that is not broadcasted online. A very mild pro to tag onto the end is no delay. Internet/data takes time to transfer.
If you're more interested in scanning as a mild interest such as being able to tune into to action as soon as you see it on the news, than an app is probably better for you. Cons about scanning is that it is harder to understand and use when compared to a super easy scanner app. It's almost never just plug-and-play, you need to work with it some to get the best performance you can with the equipment. It also might be illegal to have in your state, depending on local laws. Most places don't have a law against it, but there are a few select places that require you to have amateur radio license to have a scanner in your vehicle and such.
In the end, you are probably more likely to have your phone on you more often than a scanner. I know that in my case, I have a scanner that can monitor many things locally and that I have the choice of online feeds for things not local or for low priority monitoring.