Since that started out as a Joan Jett song, I wonder why Richie would've been involved. Desmond Child wrote a couple of tunes with her during 1988 as well, the most famous probably being I Hate Myself For Loving You.

Regarding the songwriting, you can sorta tell with some songs. Jon's not a bad guitar player as far as riffs go (he wrote a couple catchy ones for 7800°), but the sus-chords for These Days, as well as I'll Be There For You's licks just scream Richie. I guess it's safe to say that he wrote those. Same actually goes for We Weren't Born To Follow, those hanging chords somehow seem Samboralike to me. Generally, Jon is more a melody-type of guy in his writing, whereas Richie is more about textures.

There's also stuff like Damned which is pretty damn obvious IMO (Jon couldn't play the riff at all, for one), but I have no idea regarding stuff like the piano ballads, since they're usually rather reduced in terms of harmony.

There's also stuff where you can tell neither did much, such as the Desmond Child-tracks from the 80s, or It's My Life.

Either way, these guys should just adapt the Jagger/Richards model already, where both get credited all the time either way who wrote it.