My answer is more as a user than a strict comparison as you do, so the perspective will be a bit different and less precise.
Liquid I think has different goals. On Liquid you can trade Microstrategy stocks for example, so there are goals to make it a platform for traders. There is USD and EUR, and I think JPY too (not 100% sure). With Liquid since it is supposed to be pegged to Bitcoin there is no time frame for operation, in comparison to Fedimint where a community in essence can end tomorrow if it is decided to do so. Of course if the community is a village or a small town for example, we could assume it is forever.
Whereas with Liquid we can trade stocks, currencies, and save fees on Bitcoin when refunding our lightning channel, on Fedimint I feel like don't aim to be a financial platform for traders for example but rather the goal is more like giving money to friends in a community, and the overall feels like Grab, and maybe WeChat (from what I have heard of it), and everything-app competing for convenience, which was not the case on Bitcoin until then. Lastly regarding Lightning channels, you could say we could also refund our channel from a Fedimint but I don't think this is an intended use-case.
Fair enough, I was looking so far at both from the perspective of being able to make faster bitcoin transactions. If trading other tokens is the goal, then I definitely see how liquid is more suitable for this.
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If you look at it only in terms of transaction speed, then the comparison doesn't hold anymore I believe. Fedimint is definitely the one to use, not Liquid. I think also the ability to do offline transactions through ecash on Fedimint is definitely amazing, like bolt cards. Well this is half true since the vendor has to have internet but the buyer can buy offline instantly. In my case I am still very at attached to the self-sovereign aspect so I prefer Lightning but Fedimint is faster. By the way I don't know if you know but you can try by yourself the Fedi app with federations available on Mutiny.
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I use federation on mutiny
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Quite nice, isn't it? I think the Fedi app is better, at least at the moment: https://www.fedi.xyz/builders The integration with Bitrefill is really nice.
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