Unconditional welfare considers where the dynamic system will be in the long-run. Say you want to know whether the introduction of a tax is beneficial. When you compare unconditional welfare, you are asking what welfare in the new regime will be once it has settled to its new long-run equilibrium. That may be very misleading if there is a long transition period.
Conditional welfare in contrast considers welfare when starting at a particular point in the state space. So you can consider what happens if you introduce a tax, but you are still at the state values of the old regime.