Engineering degree programs have continued to dominate the scholarship funding or grants across many universities. I am not sure if the reason is largely because Engineering as science is tied to all aspects of science. Most research topics in Engineering are carefully selected to address or solve real world problems.
By applying for some of the PhD or Masters degree scholarship positions, you will notice that the requirements demand that the candidate not only have core engineering background but also have experience in software development, physical sciences or social sciences.
Most fully funded Engineering scholarships are research based. This means that the student will be expected to complete full course work as well as conduct practical experiments to demonstrate the knowledge obtained from course work. The expectation is always that the experiments will be performed in line with industry standards with particular focus to using the experimental results to invent ideas or products or most importantly to contribute to the scientific body of knowledge.
As a result a student applying for a fully funded PhD or Master degree scholarship should be prepared to demonstrate experience in the proposed area of study. Depending on the school, a research based Masters Degree scholarship can range from one to two years while a PhD scholarship funding can be from two to five. In fact in Most North American schools, Masters Degree programs are two year programs while PhD is a minimum of four years.
In Europe however, fully funded PhD degree programs can be completed in three years. You can easily find scholarship grants for Masters Degree programs but the funding may not be as extensive as PhD grants. There are also other Masters Degree scholarship grants that are a stepping stone to acceptance into PhD scholarships. Such programs may or may not be fully funded. In some cases, it covers only 50% tuition and the student will be expected to make up difference. In fact such programs can be competitive and are used as an evaluation criteria to determine if the student can be accepted into a fully funded PhD after their first year in the program.