Does a tomato plant grow faster with artificial light or natural light?

As long as the artificial light you use emits the full-spectrum of light, the plant can't tell if it is natural or artificial. What you can do with artificial light to promote plant growth is extend the length of the "day". If you leave the lights on all day and night the plant will grow faster, but keep in mind that plants also depend on cues from day length, nighttime temperature and soil conditions to "know" when to set flowers and fruit, how many flowers to set and how much sugar to concentrate into the fruit. So you might get a really fast, really tall, really green plant with little fruit. In Addition: i agree the really tall really green plant that grows to fast because you have had the artificial light on for more hours than natural light is a condition called "leggy" and this type of plant is a very unhealthy plant. What you want is a stocky thick at the base plant.