I have found that, of the three, fishing is by far the most inferior, at least on my server (I have not done the desynthesis thing, this may change things here soon). I use a different bot (thinking of picking this one up too), but mining and botany are about identical. If money is what you are after, shards (on my server and I assume most fire and wind are the highest priced) are the best ones to go for - though they stop leveling you pretty quickly.
I used one of the field manuals every chance I got (that I was paying attention) from level 1-30 (after 30 they aren;t great IMO) and just grinding, no turn ins, from 1-50 in something like 30 hours of running the bot. Fishing certainly took longer, maybe like 48 hours or so, and wasn't/isn't nearly as profitable.