Use both. For one thing, Adsense has a $100 min payout which takes forever to reach, if you ever reach it.
If you use HP earnings, you can also use HP Amazon program and earn higher commissions than if you use your own account, but you do give up some perks this way. You cannot track anything when you use HP Amazon program. You don't know products that are clicked on. You cannot select your own tracker ID. Amazon does not pay you directly. With HP program, your sales commissions is also part of your monthly earnings, but there is a delay in Amazon payments regardless if you use HP program or your own Associate program. You can also opt in for eBay as well with HP program.
Using HP earnings does not stop Adsense earnings from accumulating, 2 separaate entities.