The only thing I'm hesitant about regarding the PSR-S models is whether you can choose the Style via MIDI. As long as you don't absolutely need to select the desired Style from the computer, I think you should be able to do everything else from the computer. But I think that with the PSR-S models you must select the Style using the keyboard's panel controls.
With the Tyros, you can select a Registration using Bank Select and Program Change messages, which is how you normally select a Voice-- a timbre, tone, program, patch, or whatever you like to call it; Yamaha calls it a Voice. Or if you have a Yamaha synth-- MOXF, MX, etc.-- then you can select a Performance the same way. Basically, a Performance and a Registration are very similar to each other; they save the instrument's current settings so you can quickly recall those settings at a later time. And even though there are (as far as I know) no Yamaha SysEx messages that let you directly select a particular Style via MIDI, you can save the currently-selected Style in a Registration-- along with all of your selected Voices, etc.-- and then you can select a particular Registration via MIDI, which lets you indirectly select the Style, Voices, Effects, etc., all in one easy operation.
Unfortunately, the PSR-S models don't have that feature. Yes, they have Registrations. But I'm pretty sure they don't let you select a particular Registration via Bank Select and Program Change messages the way the Tyros does. That means you'd need to select the Voices, Effects, and other settings on an individual basis, since you can't just recall all of them at once by selecting a Registration via MIDI. And since there's no way to select the Style that way, I don't think you can do what you originally spoke of on the PSR-S models.
On the other hand, as long as you don't need to select the Style remotely, you should at least be able to select most all of the other settings on the keyboard, albeit you'll have to set them one at a time rather than in one fell swoop.
An alternative might be to create Music Finder entries for your song lists. Music Finder is a feature of the PSR-S and Tyros models that lets you create a database of song titles, where each entry is a lot like a Registration in that it specifies which Style to use, which Style Section to start with, the Tempo to use, etc. I'm not sure what the differences are between a Registration and a Music Finder entry as far as the specific information in it, but an obvious advantage of Music Finder is that each entry can be the name of a song, so it's easier to find a given entry as compared to trying to remember which Registration Bank and Registration Number happens to be the one you set up for a particular song.
Just to be clear, you'd need to select the desired Music Finder entry on the keyboard, because I don't think you could select it remotely via MIDI. But if you organized your Music Finder entries efficiently, it probably wouldn't be any more difficult to set up the keyboard for the next song in your set by choosing the song in the Music Finder screen, as opposed to choosing it from a list on your iPad.
