The key benefit of OnSong compared to iRealPro is that you get to include lyrics. Given that the churches I’ve been in typically use lots of songs with lots of words but the band practices and performs most of them rarely, that is essential for the worship setting. I also use it in other bands where I know the song but need a reminder of the words.
What it does less well at is indicating how the chords fit together in relation to each other. If you know the thread of the melody (and care has been taken placing the chords) it doesn’t matter most of the time but things aren’t too pretty when you need changes over a sustained word or want to indicate an instrumental section. There a grid-based program, like iRealPro, wins out. Furthermore, because chords are held in a pattern of bars with indications of tempo and style, it can also give you playback as a practise tool. That’s a win for the jazz setting in most cases.
What neither seem to do well is letting you insert actual music. What I’d really love would be a tablet-based implementation of Lilypond. If I do need some combination of dots, chords and lyrics, I’ll use Lilypond to create my notation and import it to OnSong as a PDF (losing the ability to transpose on the fly, although it would be trivial to generate a number of variants in Lilypond in the first place).
Footnote: Lilypond is a brilliant tool for engraving all manner of things musical – Open Source and free to use. However, it does require a high geek quotient – sometimes the learning curve is so steep it feels like an overhang!