Do you mean the computation of the PoW can be outsourced from the payer and the payer could pay a fee?
In that sense our designs are equivalent then. The assumption is that such outsourcing will be driven to very low profit margins near to costs. Also the payer is still in control of whom they outsource to, so control is still decentralized.
Yes, the transaction issuer can add an extra output that pays some amount to some address. If the owner of that address wants to get the money he has to attach PoW to the whole transaction. Effectively it's like fee, but it's not mandatory. Note that anyone could attach the PoW but only payment beneficiary will win from that, does it mean that "the payer is still in control of whom they outsource to"? Maybe.
I wouldn't say that the designs are equivalent because miners (or fees) were removed to make a homogeneous system. And subsidy was removed because a DAG-based coin with subsidy can't come to a consensus and find Nash equilibrium at the same time. The outcome may be the same, but the intentions were different.