Susan
There is only limited overlap between the two benefits, primarily mobility and continence, but there may still be some value.
Ask the DLA Unit for a Statement of Reasons for the new Decision this will allow you to understand, for what and why they gave it to you, you can then feed this back into the Tribunal Service as evidence.
Obviously the DLA post dates the ESA Decision you are appealing, if it is by a significant period then the panel may not take into account, as they will argue they can only look at evidence that was relevant to the date the ESA Decision was made.
Good luck
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems