It's not either-or, is it, but both-and.
Most of the time I fly a little taildragger with no flaps, very few instruments, no navaids, one radio (and a mode S transponder because you pretty much have to have one of those now).
I also have an iPad, but can't use it in the taildragger because there's no room for it if there's someone in the other seat, which there usually is.
That said, there are some brilliant Apps for the iPad, which I use for planning and when I fly something larger.
I don't know about US chart coverage, but in Europe SkyDemon has to be the top aviation app - planning, NOTAMs, weather, and in-flight GPS all in one. It also has a vertical profile strip beneath the plan view, which is very useful. It suppresses the airspace that isn't relevant to your present altitude (the charts are proper digitised ones, not electronic photographs).
Apart from that, AeroWeather Pro, iVAC if you need a French airfield guide, GoodReader plus EGXX for UK airfields, PilotWiz for the calculations (fuel, W&B, that stuff), and Compass 54 for those occasions when your primary compass decides to play games.
Beware of the apps that pretend to give you a full IFR panel. I had one but removed it: it was based on the accelerometers and compass in the iPad, not on gyroscopes etc. While it made a fair attempt at simulating an AI etc, it would have killed me quite quickly if I'd relied on it in IMC in rough weather.