I may be able to help with this as we do quite a bit of both things at our facility (kettlebell training with StrongFirst methodology as well as having a team of athletes who compete in weightlifting). We also are fortunate to have a great physical therapist who sees patients out of our facility and incorporates our equipment (mostly kettlebells) into the rehab process.
As a general statement, you will see all methods mentioned previously in this thread performed in our facility, and that holds true specifically with the weightlifting team. If you want to know which will get you the best bang for your buck in the spirit of training efficiency and in order to avoid diminishing returns you will need some sort of needs analysis. Here are some examples:
1) People who are seeing our physical therapist for shoulder pain /injuries tend to be recommended a lot of bottoms up work. I will not speak to why since I am not a clinician, but anyone who has familiarity with the work of McGill, Cook, etc. will probably be familiar with why.
2) People who can maintain reasonable rib cage / trunk position while trying to go overhead but seem to lack true shoulder mobility also get recommended a lot of bottoms up work
3) People who seem to lack overhead stability as a result of inability to maintain a strong rib cage / pelvis / trunk position tend to get "carry" variations that can get loaded heavier like rack carries or overhead carries
4) Most of our weightlifting team performs traveling lunges with one (or sometimes even two) kettlebells head overhead as these seem to offer fantastic carry over to the receiving position and recovery of a split jerk. Use good judgement on weights (especially if you do doubles) as these are usually quite hard at first. One of our lifters who has jerked 140+kg struggled with a single 16kg on these.
5) People who seem to generally not have any major limitation overhead (and want to keep it that way) generally will do whatever variations they can load heavy, since their system seems well prepared for it and their primary objective is to continually improve their body's ability to stabilize heavy load overhead.
Hope that helps
My own 2-cents as well is that if you do NOT see overhead mobility or stability as a limiting factor in your weightlifting, then probably a small amount of TGU will be sufficient for what you're looking for. If you DO see overhead mobility and/or stability as something that is a high priority for you to improve, then do a needs analysis of what exactly you are lagging behind in, and pick a training exercise to complement that.