Generally, I emphasize slow practice a lot. Chick Corea says that the way to play piano fast is to practice slowly, a lot, and classical pianists know this to be true. (The pianists Van Cliburn and Rachmaninoff are famous examples of this approach.)
I tend to emphasize slow practice for the simple reason that not many pianists embrace slow practicing enough. Or, if they do begin to practice something slowly, they soon become impatient and speed up way too soon and the music doesn't become part of their physicality in the way that they yearn for. And then they wonder "Why don't I ply as well as I want to?"
When someone recently emailed me about slow practice, however, I broadened the perspective a bit. This pianist wondered if he should stay at a slow practice and let the speed come by itself or was it best to gradually increase the tempo.
This is a great question, mostly because it's very practical and comes out of his real experience at the keyboard.
Personally, I've found that both approaches work well, and I use my
intuition as which way to go at any given time. Sometimes I will do exactly as this pianist described, and stay at a very slow tempo for a long time. I do this a lot when learning to improvise over challenging chord progressions. But at other times, yes, I gradually increase the speed on the metronome. And at other times, I'll alternate very slow and very fast, going back and forth between the two contrasting speeds.
In general, I try to be very aware when any particular practice technique becomes stale, and then try something else. This ensures that we stay interested, motivated, and "active" when practicing the piano. The key is to be consistent yet flexible at the same time. That's what will help us the most in the long run.
Enjoy the journey and "let the music flow!"