All studies I've ever seen prove that an inhaler, if used with a spacer, is equally as effective as a nebulizer.  For the treatment of mild and moderate asthma both techniques are of equal benefit for most patients as you can see from this link. 

Advantages of MDI is that it is easily portable and can be used just about anywhere.  The problem is that when an asthmatic is having a severe asthma attack he might not be able to generate enough flow to get all the medicine.  In this case, a nebulizer should be used.

Some people are not able to coordinate the MDI with spacer, such as those with arthritis, very young, or elderly, etc.  For these patients a nebulizer will work better than an MDI.