In short I just wanted to ask for clarification, is it optimal to open two channels with each peer e.g,
Or it is better to have one channel e.g,
I look forward to your advice/response.
Sincerely,
Optimality is a very strong word and in general it is very hard to make statements about optimality without properly defining what one is optimizing for and conducting a rigerous analysis.
However I can give you a few things to consider when addressing the question. Recent research has showed that larger channels have a higher liklihood to sucessfully route payments on the Lightning Network which is one reason why one might want to use one large channel instead of two channels.
On the other hand one might want to increase the overall capacity with a peer. Since splicing is not implemented yet it seems cheaper to just open an additional channel instead of closing and opening the channel in particular if one considers the downtime of the channel while being closed.
Another thing to consider are the HTLCs limits and congestions considereations which currently do not seem to be a problem but might very well be in the future. Having two parallel channels will allow more concurrent HTLCs between the two peers in comparison to a single channel and could this be considered like a parallel street.
Also there might be things with respect to privacy and protection from balance probing. As far as I know nodes with parallel channels will opt to forward and htlc that was designated for one channel through the other one if they see fit. This might help nodes to protect their channel balance better from probing attacks though I personally think that JIT-routing is the better mitigation.