This is a great question! From my knowledge I think the only real difference in the Designer reconcile is that you get to put your own custom subtasks on the Reconcile Design task in the Process Framework Admin Tool.
Another reason to use the Designer reconcile would be to limit its use to certain state in the workflow by setting up the Reconcile Design task in the Px Admin Tool according to your business rules.
Here's what the out of the box Reconcile Design subtask does (found on the help page here):
Reconcile Design reconciles the parent version to the current design.
- MMWorkflowManager must be the current extension.
- Workflow Manager must be open through ArcMap.
- The selected node is a design node.
- The user must have an editing session started in ArcMap.
- A design must be open in ArcMap.
- Reconcile target must either be default version or a postable version.
- Determines whether the DefineConflictsByColumn configuration value is set in the Process Framework Admin Tool. If this value is set to 1, conflicts are defined by column. If this value is set to 0 or not set at all, conflicts are defined by row.
- Reconciles the parent version to the open design.
Could it be the case where those designs have a different parent version other than SDE.Default? When you use the ESRI reconcile button are you always picking SDE.Default as the target version?
Hopefully someone else can answer the question on the other things that the Designer reconcile process might be doing extra that would make it required to be used instead of the ESRI reconcile.