I don't think there's a rule that will necessarily work for everyone. For me, doing several different things seems to help. I start off hands separate at a moderate tempo. Once both hands are comfortable I put them together at an even more moderate tempo. When it feels comfortable I start to increase the tempo a bit. At that point I have the feeling of coordination in the hands, but to get faster there are refinements in the motions of each hand that I need to make. For that I work hands separate and try to push the tempo up a lot.
Since I find that I am often slow because my fingers don't get off the keys fast enough, I'll play the passage with a sharp finger staccato (being careful not to tense up the hand while I'm doing it). That gets me used to getting off the keys quickly. When I pay careful attention to how that feels, I often am able to identify where, exactly, I had been slow in getting off the keys, because at that spot there'll be just a little less sharpness in the finger staccato.
Then I try a whole bunch of rhythms, 2-rhythms (long-short and short long), 3-rhythms (long-short-short, short-long-short, and short-short-long), all the way up to every permutation of 7 rhythms, with the short notes played at or above the tempo you're aiming for. It's helpful to write in the fingering of every note before doing this. I find that it's easy to hear what's going on in the short bursts of speed so that I can tell whether I'm playing evenly, whether something is uncomfortable or tense, etc, more easily than if I'm trying to rip through the whole passage at speed. You can relax fully on the long note and that will train you to relax when playing the whole thing fast. At the early 2 and 3 rhythms you can also pay close attention to exactly how you are hitting the key - are you hitting it dead center or just barely catching the edge? Finally, if you play the passage in all these rhythms, you will have burned it into your memory much better than you would from just the muscle memory of playing the whole passage. Pay attention to how things feel and if some particular group of five notes, say feels awkward, play around with the motion you are using until it feels good and comfortable.
While doing all the above, I also put hands together sometimes to make sure the coordination is still there as I up the tempo. Then, if coordination is a problem at the higher tempos I work beat by beat or measure by measure, hands together, overlapping the bits I'm working on and working at speed. Working on small bits like that makes it easier (for me anyway) to hear where alignment or coordination problems are cropping up. Gradually I put everything together until the whole passage is done.
This is just what works for me. There are people who swear by only ever practicing hands together. I've tried it and it did not work as well for me as the HS approach I described above, but it might work for you.