Commerce on the Internet has come to rely almost exclusively on financial institutions serving as trusted third parties to process electronic payments.
Payment channels, as described by the lightning network, are optional.
The mempool on both chains are practically empty and both chains function the same, until the mempool is full.
One chain will allow for optionally greater throughput via payment channels and possible a block size expansion.
One chain will allow for block propagation upwards of 8 megabytes.
Neither relies exclusively on third parties. The first mentioned chain has an optional ironic future where everyone operates a payment channel and eventually consolidates into one payment channel provider, I guess.
Both chains have other "threats" towards centralization.
The connection between full blocks and transaction fees is here:
if it wasn't clear, I was writing that they are practically empty right now. at the time of writing.