Sex is a combination of the physical and mental. How much sex is affected by either process depends on why and how you are having sex. When having sex with a partner the physical and mental motivations will be very different to those of someone who is having sex for more personal reasons.
When having sex with a partner you should ideally be combining both physical and mental processes. The best sex starts before any physical processes happen. This is because mental states are extremely important when having sex with a partner. Having a nice meal together, spending time together watching a movie (can be on TV/DVD) and having that general closeness should put you on an even level mentally. Being relaxed makes the sexual experience more pleasant (for most). One of the best ways as indicated in a recent survey to prepare for sex is to have a shower either alone or together. Over 25% of men and 30% of women said this makes them feel the sexiest.
Good sex should be a physical thing long before it enters the bedroom, with touching stroking and general embrace. It is possible for both men and women to have orgasms without direct stimulus to genitalia, and while being fully clothed. This requires a high level of mental awareness or closeness. Arousal is very much a mental state, but has a definite physical connection.
When having casual sex motivations are very different and do not require a very deep emotional connection. Both parties still need to be aware of their mental processes to ensure arousal. In the case of casual sex the physicality is the biggest goal and often the determining factor. Mental states are also likely to be playing a huge part. Sex may be a way for some people to find mental security. Sex may be a way to make themselves feel better or escape problems. Casual sex may just simply be a good time both physically and mentally.
Children cause big changes in your sex life. Children are both physically and mentally draining. This should never be a reason to end you sex life, in fact this should make your sex life even more important. You can always make time, by sending your children to a friends or relatives or when they are on trips or when they are in bed and asleep to have sex. This sex should be used as a way to be physically and mentally close and to strengthen your bond.
In terms of which is more important, the answer is neither. It is the combination of the physical and mental which makes sex great.