Both methods will give you an N1 setting that's less than what you'd have if you used actual temperature & no derate (i.e. max takeoff thrust). The computations to get to that N1 setting are different, but at the end of the day, the pilots (or the autothrottle) sets a particular N1, and you go fly. Which method, derate or assumed temperature, or both, that you used to get to that N1, isn't really all that important.
For the pilots, the company will probably tell them which method to use. Or the performance computations will consider whatever permutations are out there, and spit out an answer -- derate to XXk, assume temp of YY degrees, or maybe both. And the pilots put that into the FMC, and you go fly, knowing that the N1 that you get at the end gives you enough performance to do all the things you need to do: 35' at the end of the runway if you lose one at V1, meet obstacle clearance criteria, etc.
The derate method is typically less granular than assumed temperature -- you have two or maybe three derate setting you can select, and that's that. But those steps may be pretty big steps. The software can step an assumed temperature up one degree at a time to find exactly the minimum power that's needed to meet all the criteria. But there is some limit to what temperature you can assume, and if you have the really light airplane on a really long runway, even assuming that max temperature may give you lots of performance to spare, and so in order to bring the thrust down to being only what you really need and no more, you need the bigger "bite" of a derate.
There is a human factor to consider, in that if the crew is selecting a derate and entering an assumed temperature, you want to be sure that they did that process right, and (particularly if conditions or runway change) you don't end up with the wrong combination of derate + assumed temperature. If Plan A was to derate two steps down & use the actual temperature, then Plan B was to derate one step down & assume 45 degrees C, the hybrid of not changing the derate (leaving it at two steps down) AND assuming 45 degrees C will give you less thrust than either Plan A or Plan B, and you want to make sure that an error like that can be reliably trapped.
But again, that sort of decision of what method(s) are used is made more by the company and the performance software than by the individual crew. As a pilot, put what you're given into the box, verify that it's right, and go fly. I'm not overly concerned which computational path the software used along the way to telling me to set 88.3% N1.