If a person is designated as the only beneficiary of all funds and there is an existing older Will stating other distributions, which takes priority?

I cannot tell for certain from your question - is the "person designated as the only beneficiary of all funds" designated in a will?  If so, the more recent will takes priority IF the older and more recent provisions are inconsistent with each other (it sounds like they are, but of course I am not looking at the two wills) or the more recent will states that the older will is revoked.

If the "person designated as the only beneficiary of all funds" is designated in a retirement account, life insurance policy, bank account, or similar item, then that designation controls over a will.  A will only controls things that fall within the decedent's estate.  Financial accounts and insurance policies that name a beneficiary pass outside the estate.

It is important for people to understand this, and they often don't understand it.  If you name someone as a beneficiary, that person is going to get the asset no matter what your will says.  If you put someone else's name on your account, that person is going to get the account no matter what your will says.