Both will work, in the sense that you will get beer at the end, but they will have different results.
The 160F steep for a few minutes will not extract much sugars from the base malt, and those that are extracted will be dextrins, non-fermentable sugars that give body, and also starches which will give the beer a haze. Combined with the use of extract which is generally high-ish in dextrins already, the additional dextrins from the steep would make the mouthfeel would be thicker than normal for an APA.
The 150F 45-min mash followed by a 170F sparge will extract more sugars, in particular, fermentable sugars, and the longer step gives the starches time to break down into simpler sugars, so no starch haze. The low temperature also favors production of simpler sugars rather than dextrins, which are fermentable, leading to a lighter body. The 170F sparge rinses the grains of these sugars, increasing yeild, and stabalizes the enzyme activity.
With 1/3 base malt in the recipe, my money would be on mashing.