zlacker

One thing that comes to mind is function application, which begets recursion. This is the last quarter of the example program's encoding, while the example TM has enough space for 6 states and no concept of a "goto" or "jmp" that would simulate recursion.

>>tadfis+(OP)
On the contrary, 36 of its 60 bits are dedicated to goto labels. Although you're right that TMs cannot "call" a state then "return" to the caller, as would be expected from a reusable function. Regardless, for busy beaver purposes, most of TMs' state tends to be encoded in the tape rather than the state graph, so I suspect it's the differences in the means of data manipulation that create such a gap. (E.g., with substitution, you can easily move a term across an arbitrary amount of garbage.)