Do I level up a spell faster by casting often or by casting longer?

I could find no credible sources about this, so I performed a completely unscientific experiment to figure this out:

I loaded up a low-level saved game and used Flame continuously until my magicka was exhausted, then took a screenshot of the skill screen. I then reloaded the game and used Flame in ~1 second bursts until my magicka ran out, and took another screenshot. I then compared the pixels in the screenshots using Paint, and determined that they had both advanced an equal number of pixels. This suggests that it's extremely likely that it doesn't matter if you cast with duration or frequency - you'll gain at the same rate.

In summary, there is most likely no difference.

With respect to Destruction magic specifically (as well as most combat skills), you gain skillups not by casting more or for longer, but rather by doing more damage.

You'll skill up faster using a more powerful spell and simply being effective in combat than you will by trying to grind on rats with starter spells.