NEXT Sapphire is difficult to evaluate because its power depends on a lot of variables:

• Obviously: How many NEXT Ice do you have rezzed? If this is your only one, it's an okay facecheck penalty, whereas if you've already rezzed another it can be brutal. But if you have other NEXT Ice rezzed, they know you're probably running NEXT Sapphire, and it won't be much of a surprise.
• Do you actually want to draw cards? In CI the answer is almost certainly yes, but in other decks it's not as clear, and the first subroutine might be pointless.
• Do you have cards in Archives to bring back? If this is turn 1 and you didn't get to play e.g. Hedge Fund, the second sub isn't going to do anything. On the other hand late-game it could bring back several Biotic Labors or something else that's game-deciding.
• Are there cards in your hand you want to get rid of? If this is a run on HQ then this is very relevant, as you can bury excess agendas you don't want to have stolen. If this is a run on R&D, it could let you decrease the agenda density in R&D. But maybe you want to keep all your cards!

The nice thing is how these synergize. If all of them fire, or even just both the first and the last, the downsides for the first and last subroutines negate each other, and Sapphire lets you adjust your hand quite nicely. Oh, and there's always The Twins (plus probably Helheim Servers) for an "infinite" combo to trigger all of the subroutines an arbitrary number of times. (Helheim to make it unbreakable, then recursively using The Twins and another copy of NEXT Sapphire in HQ/Archives, probably playing this out of CI.)

HOWEVER, there are downsides to NEXT Sapphire that are not obvious at first.

The primary weakness: Usually one of the subroutines is fairly harmless, especially to let fire repeatedly. If you're running HQ, letting them draw cards could populate their hand with more agendas to steal. If you're running R&D, letting them shuffle cards back into R&D is probably fine, and usually doing it more than once is redundant. Alternatively, letting them draw cards might be irrelevant if you just want to flood HQ. (So ideally play this in a deck that always wants to draw.) Or maybe you don't care if they take any of their trashed cards back for some reason.

The subtle flaw: As the rules stand today (April 2018), the third subroutine is mandatory. Sure, you may choose to shuffle 0 cards from HQ into R&D, but that still shuffles R&D. For example, when Jackson Howard was around, you could choose to use him to "shuffle 0 cards in", just to shuffle R&D, as per this ruling. That was great when you had control over the effect, but now it makes NEXT Sapphire a very dangerous piece of ice to put on R&D, or potentially on the outside of a server, since it gives the runner the power to shuffle R&D, whether that's to see a fresh card off the top or because they want to stop you from drawing something they've seen.