Intermittent fasting and calorie restriction are two ways of reducing your calorie intake to obtain health benefits. Intermittant fasting might be accomplished by eating every other day, for example, while calorie restriction means eating every day, but eating less. In both cases, you have to make sure your intake of micronutrients is optimal, and your physician agrees, as for any sane dietary choice. On the scientific side:

Both calorie restriction and intermittent fasting produce significant health and longevity benefits in shorter-lived mammals such as mice, and at least significant health benefits in primates, including humans.

Far more research has been accomplished for calorie restriction, and uncertainty remains as to whether intermittent fasting is as good, definitely increases longevity, has a preferred method of practice, or whether it could even be harmful to long-term health if done incorrectly.

It seems plausible that calorie restriction and intermittent fasting produce their benefits in similar but different ways, based on research in lower animals, but I know of no research confirming this in mammals.

From the point of view of actively practicing either intermittent fasting or calorie restriction, intermittent fasting is much easier for anyone whose eating habits interact with those of other people, or who is already fairly set in his ways with good dietary habits. You just don't eat some days - very simple, and few other changes to the routines of life are needed.

Starting to practice calorie restriction, on the other hand, requires greater effort and more thought in terms of changing your diet. It's not hard, especially given the good resources available to walk you through the obvious pitfalls, but it isn't as simple as just saying "I'm not eating right now."

So the traditional trade-off in labor and knowledge:

Intermittent fasting is usually much easier to introduce into your life, but has far less scientific support or a body of research to indicate the optimum methodology.

Calorie restriction requires more initiative to organize, but has a great weight of science backing it up, and a wide range of resources based on decades of practical experience.

Given what I know of human nature, I suspect that intermittent fasting will rapidly become more popular than calorie restriction as soon as it accumulates a little more research in mammals than presently exists.