I was unclear in the setup: the utility function isn't supposed to reflect a representative agent for all humanity, but one individual or proper subset of individuals within humanity (if used to be "the human utility function," then you are certainly right that only xs would be produced after everybody in humanity had 1 y, for either U-function).
Imagine we make 100 more units of x. With the second function, it doesn't matter whether we spread these out over 100 people or give them all to one, ethically--they produce the same quantity of utility. In particular, the additional utility produced in the second function per x is always 1.
In the first function, there is a serious difference between distributing the xs and concentrating them in one person--a difference brought out by sum utillitarianism vs. average utilitarianism vs. Rawlsian theory.
I use e^x as an example, but it would be superseded by somebody with e^e^x or x! or x^^X etc.
You seem to be assuming that your U(x) is per-person, so that each person a would have a separate Uₐ(x) = xₐ + log yₐ (or whatever), where xₐ is how much x that person has and yₐ is how much y that person has.
You then imply a universal or societal "overall" utility function of the form V(x) = ∑( Uₐ(x) ) over all a.
Your fallacy is in applying the log transform to the individual Uₐ(x) functions rather than to the top-level function V(x) as a whole.
I just came across an essay David Friedman posted last Monday The Ambiguity of Utility that presents one of the problems I have with using utilities as the foundation of some "rational" morality.