Level 6 Valued Member
Almost any full body resistance exercise is an excellent assistance for strength, broadly speaking.There is no "vs" to be had here. Both are excellent assistance for strength. The bottoms-up clean, without carrying, is an excellent exercise, as is the bottoms-up press. I like both in sets of 5-8 reps with a bell only slightly lighter than I would press. The rack carry is also excellent. Look up the Cook Drill - overhead carry into rack carry into suitcase carry.
Asking which is better is like asking whether it's better to squat or to deadlift - both are good, some people do only one, some people only the other, and each has its place in many training programs.
But when looking for training specificity, as opposed to GPP, it's helpful to ask "what is this move best at training?". We all only have so many hours in a day, and when creating programming, there are trade-offs.
The Cook Drill was mentioned above, as well. I agree that looks interesting and will give it a try.