https://en.wikipedia.org/wiki/Optical_amplifier
In the end it is probably mostly a matter of how many hops that will determine which is the faster path, the two paths are mostly equal in other respects, I suspect the latency incurred for each hop is roughly the same, assuming they use error correction and re-transmission on the link layers between the satellites.
If it all gets passed through blindly then it will be a bit quicker because there is no decoding step involved but I highly doubt that because it would lead to substantial inefficiencies and loss of capacity (the difference between a switched and hub). Smarter to be a bit slower and to maximize the routing capabilities of the satellites so as to optimize for the scarce resource: inter-satellite bandwidth.
I'm quite curious to see what their antenna setup looks like in practice that's going to be an engineering marvel.
https://en.wikipedia.org/wiki/Laser_communication_in_space
But optical signal amplification is a trick that really only works when you are on a very long run where the signal gets attenuated to the point that you need to boost it. There is no routing option in such a system, it is essentially point-to-point with in-line amplifiers.
So even if they may use laser based comms I don't think optical amplification will be used, the more likely avenue is to decode the optical signal, decide where it has to go next and then fire off another burst.
Alternatively they may use radio waves instead of lasers, I'm not sure what system SpaceX will use for this particular system, given the accuracy required for laser based communications I would assume they will use radio.
https://www.cnet.com/news/spacex-starlink-satellite-broadban...
We were planning on tracking satellites in adjacent orbital planes (which were orbiting in the opposite direction) as well as in-plane. So, yeah, moving parts.
Whenever this topic comes up, I wonder what happened to all the work we did at Motorola in 98-99. There were several hundred engineers in Tempe generating thousands of pages of design documents for over a year. We archived all our work in spring 1999 sand were all shuffled off to other projects.