The first thing I would say is that you cannot separate nutrition and training. The two work together synergistically and regardless of your goals - gaining muscle, losing fat, athletic conditioning, whatever. You will get less than-optimal or even non-existent results without paying attention paid to both.
If you're a beginner and you don't posses nutritional knowledge, then mastering nutrition is far more important than training and should become your number one priority. I say this because improving a poor diet can create rapid, quantum leaps in fat loss and muscle building progress.
If you're still eating lots of processed fats and refined sugars, cutting them out and replacing them with good fats like the omega threes found in fish and unrefined foods like fruits, vegetables and whole grains will make an enormous and noticeable difference in your physique very quickly.
No matter how hard you train or what type of training routine you're on, it's all in vain if you don't provide yourself with the right nutritional support.
The muscular and nervous systems of a beginner are unaccustomed to exercise. Therefore, just about any training program can cause muscle growth and strength development to occur because it's all a "shock" to the untrained body.
Eating more than six meals will have minimal effect. Eating more protein ad infinitum won't help. Once you're eating low fat, going to zero fat won't help more - it will probably hurt. If you're eating a wide variety of foods and taking a good multi vitamin/mineral, then more supplements probably wont help much either. If you're already eating natural complex carbs and lean proteins every three hours, there's not too much more you can do other than continue to be consistent day after day...
Except for the changes that need to be made between an "off season" muscle growth diet and a "precontest" cutting diet, the diet won't and can't change much - it will remain fairly constant.
According to powerlifter Dave Tate, an advanced lifter may adapt to a routine within 1-2 weeks. That's why elite lifters rotate exercises constantly and use as many as 300 different variations on exercises.
So, to answer the question, while nutrition is ALWAYS critically important, it's more important to emphasize for the beginner (or the person whose diet is still a "mess"), while training is more important for the advanced person... (in my opinion).
Once you've mastered nutrition, then it's all about keeping that nutrition consistent and progressively increasing the efficiency and intensity of your workouts, and mastering the art of planned workout variation, which is also known as "periodization.