I don't think there is an equivalent, sadly. The Merkur adjustables seem to be very different beasts by all accounts, but I only have experience of Gillettes, so I'm sure others will fill you in on that.
Briefly, the Fatboy is a vintage Gillette twist-to-open adjustable razor, with nine settings ranging (subjectively) from ultra mild to sensibly "aggressive"; it has a relatively short but thick handle, hence the name, and is decidedly heavy. The general impression you get is of a high quality item with nice tactile feedback - I'm starting to sound a bit fetishistic now, but they really are very desirable razors: even the clicking of the adjustment mechanism sounds just right. A mint one might set you back £40, but probably a bit less; alternatively a Slim (same general description but with a longer, thinner handle) commands a lower price, say £25 tops. Somehow or other, I now seem to own one of each, and they shave very nicely indeed, thank you. Highly recommended. Here's some information from another forum which might be of interest if you haven't seen it yet:
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