It seems as though the only thing that my villagers like to do when I shut off the game is populate the island. That is why I tend to pause the games I am most interested in when I know I'm going to be gone for more than a half hour.

As for, which is faster. I think they go basically the same. Village Monk is right in the fact that some people may suffer from the watch pot syndrome, and are happier by turning it off and coming back. Then there's some who rather have it close at hand so they can check back at any time.

I have had a scenario where I had a bunch of villagers researching, and my tech points were racking quite slowly. I took several off and put them on farming, keeping only some of my masters. Doing so caused my tech points to make a huge leap as far as the speed they wer racked up goes.