I see this one a lot, mostly from the people who want Josh back in the band, this is one of their reasons.
In my personal opinion Josh and Taylor are pretty evenly matched in terms of songwriting, then again when I think of my top ten Paramore songs 8 of them are songs by Josh.
It could be argued that Paramore's lyrics, while they haven't lessened in quality, have become more simplistic. The songs, while Josh was writing, were always darker themed, Taylor's songs are more simplistic, both use metaphor pretty well.
Decode
How can I decide what's right
When you're clouding up my mind?
I can't win your losing fight all the time
Nor can I ever own what's mine
When you're always taking sides
But you won't take away my pride
No not this time
Not this time
Ain't It Fun
Where you're from
You might be the one who's running things
Well, you can ring anybody's bell to get what you want
You see, it's easy to ignore trouble
When you're living in a bubble
So what are you gonna do when the world don't orbit around you?
So what are you gonna do when nobody wants to fool with you?
When Taylor writes a song directed at someone or something it usually takes a more fun, teasing, and sarcastic approach in songs like Ain't It Fun, Fake Happy, and Rose-Colored Boy. Where as Josh tends to write from a more serious, and some would say bitter perspective, like in Decode, All We Know, and Playing God. Of course both of these are also influenced by Hayley's mood when writing.
Musically as well they're both very different, once again Josh's muisc always sounded dark and moody, there was always a guitar solo somewhere. Taylor's idea of melody is very light, very tropical, it incorporates a lot of different elements
I'm not saying I want Josh to come back to Paramore, I wouldn't necesarily be against it though. I just think of a song with very dark complex lyrics written by Josh against a fun bouncy melody written by Taylor, I think it could be really cool.
In my personal opinion, they're both different, and they both have great things about their writing, and they both compliment Hayley really well.

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Paramore Conspiracy Theories
RandomJust some things I've always wondered/ been curious about with Paramore. The most recent of these that I'm sharing is going to be about Jeremy "leaving", so I'm breaking my promise a bit. Some of these are my own, some I've found online, a...