SEH,
First our condolences to you and your family.
With regards to your question, you should not wait for the VA to make a decision on the veteran's claim. The VA could look at that action as a form of attempted fraud. Once you file either the 21-530 or the 21-601 form, the VA will stop the processing of the pending claim and close out the file.
There's no useful purpose to delay in notifying the VA of the veteran's death. Previous correspondence from the VA, in fine print, instructed the applicant to keep the VA informed of all changes.
As far as the question being asked, both forms need to be submitted because there are two separate benefits being applied for. The 21-530 form is for the allowance that the VA provide for qualified veterans for the '*burial allowance and the plot allowance*'. The 21-601 form is for what entitlement was due to vet at the time of his death.
21-601 needs to be filed by the person whoever paid the expenses, and provide proper documentation of receipts, etc.
For a more in-depth explanation of this, please see this question on the FAQs
http://veteranaid.org/faq/index.php?action=artikel&cat=3&id=15&artlang=enAgain, our condolences to you and your family with the hope you will be able to close this final chapter and allow yourselves time to deal with your loss.