In the end it works about the same, in my oppinion.
With the ADJ strip you need a ULN2803 IC to run it, but have the AC side pre-assembled and in a casing. You buy that with possible quality issues, although I do not recall anybody else reporting those issues before, so I could not tell how often those arise.
With the 5V relay board you should probably use a ULN2803 IC as well, since every activated channel puts some activation current through the PI‘s pin. In total I think there should not be more than some 60mA or so running through all GPIO pins in total, so these relay channels might put you closer to this than you are comfortable with. At least that was the case for me, although I might just be paranoid, since there have been a few people ( including the leviathan board) that run 8 channel relay board directly on the pins seemingly without issues.
With a 12V board you would definitely need a ULN2803 in between, although the 12V boards are much less common because of that.
Downside is of course that you have to do the AC wiring and casing yourself, which comes with some risk, I would say.