Both methods are equally valuable. They are different tools that accomplish different things. Let me give an oversimplified example. Imagine working very hard and spending lots of time on a piece. You learn to play it well at a snail's pace. Gradually the tempo increases as you do all the right things, meditating on comfort, ease of movement, etc. After a long while, you finally realize that there are many places that your left or right hand fingerings do not work. Oops!
Being sensitive to those types of places, it is a good idea to play small sections up to tempo almost immediately to find fingerings that work. Somewhat off topic, I also use the technique to discover good fingerings. Rather than trying out certain fingerings, I will just attempt to play the passage up to tempo, and as musically as possible. After I am satisfied, I will then study what my hands were actually doing so that I can "learn" the fingerings I want to use.
There is a lot more to it that just what I wrote. The slow careful practice is no doubt valuable and is a good segment of my practice time. However, the fast practice (in as small of sections as necessary) not only requires fingerings that work, it also forces the inner and outer poise to be more refined.
Dr. Todd Tipton, classical guitarist
Cincinnati, OH, USA (available via Skype)