You will want to buy the 10 delta calls and puts vs selling the at-the-money calls and puts when implied volatility is high vs your view on realized. You are selling vol which means that your view is that volatility will be lower than that implied by the markets (your maximum profit will be if the underlying doesn't move (no volatility) and you end up collecting the premium from selling the at-the-money straddles vs buying the 10 delta strangles (10 delta options are cheaper than 50 delta at-the-money options).
If you just sell the straddles, you will collect more premium since you will not have paid premium for the 10 delta strangles. However, you will have a different risk profile. If you are incorrect and realized volatility is much higher than you sold it (ie the underlying appreciates or depreciates by a lot), your losses will be unlimited with just the short straddle. The cheap strangles protect you from a extreme volatility of your underlying by limiting your losses.