The difference is that in the secondfirst example, successFn will not get the callback function arguments. Neither will the this object be the same; in fact, it will be window rather than whatever may be specified as the context for the .ajax() call if the function is not a member of an object (in xyz.successFn(), this would be xyz).
The secondfirst approach is less concise and possibly slower; by "wrapping" the function, you are quite possibly using more browser memory and CPU time. I wouldn't use the secondfirst approach unless you are paid by the line of code or you need this to point to an object that successFn is a member of.