TeX people often claim that you can enter math faster in TeX than in MathType. However, they often just say this with no evidence to back it up. Often they have years of working with TeX, try MathType after working with it for 15 mins, and then claim that MathType is much slower.
They also assume because you can pick symbols and structures using the mouse to buuld an equation that you have to. MathType defines keyboard shortcuts for virtually everything and let's you redefine them according to your own scheme. They are much shorter than TeX's keywords so fewer keystrokes are required. Finally, if the user happens to know TeX for an expression, they can enter TeX language for most things.
Many TeX people claim efficiency because they rely on a library of TeX macros they'be built up over time. This increases efficiency by taking advantage of the repetitiveness of most math. MathType has a roughly equivalent feature with its customizable toolbar. It can't do everything TeX macros can do but it has one big advantage over them. You can create them on the fly. Macros mostly require forethought since creating them takes one away from the task at hand. In MathType, if you see that a subexpression you have entered is going to be needed several times later, in the same equation or in subsequent equations, you just select and drag it to the toolbar. Later, when you need it, just click on the toolbar cell and it inserts the subexpression.
My company, Design Science, makes MathType so I am definitely biased. I will say that TeX does a wonderful job of formatting math. And I mean no disrespect to Donald Knuth and the TeX community in general.