Hard new ideas VS Hard technical ideas? I'm a CS master student. During my early days looking for a thesis I noticed two categories of projects:


Projects a about completely new idea.
Projects about improving an existing technical concept.


By the first one I mean completely new stuff (something I'm doing now as my thesis). Such projects require intensive thinking to formulate them and put them into academic contexts and logics. While a lot of the time will be used to try and test new things as well as justyfing and putting the results into proper academic context and logic, very few time could be spent learning advanced stuff regarding your field.

In the other kinds of projects one would need to improve the running time of an algorithm or its performance. Such projects would require the student to go into very deep stuff regarding his field and become really advanced.

Now that I'm doing the first kinds of projects, I started to feel unconfident about myself and my skills when I see how the skills of other students who worked on the second type became. The reason behind that is I feel that my effort doesn't show up to people when they will probably read my thesis. Because they won't see advanced mathematics and algorithms as in the second type. How should I deal with this personal problem?
In general, the answer is: Provide the landscape of your field, and show how the new-ground you are covering is missed by other people who passed the question by. 

If your thesis is a branch of of another topic, then show where the branching occurs, and how people on the dominant branch missed it; If your topic is truly novel, then show the problem its solving and why you found it interesting enough to spend a year or more of your life on it.

I have a feeling that intuitively you know the answers to these questions; get them out and people will understand why your thesis has worth. 

90% of the advice from your last question still applies; It's incredibly difficult to do an apples to apples comparison between degrees, even under the same supervisor. 

The crux of this question in my mind, which prevents it from being a duplicate, is how to present new-ground while avoiding comparisons to other work which has a stronger theoretical background. 

A important part of the answer is almost certainly going to be 'Sit down and talk with your supervisor about this concern'. That's what they are there for. They will have a clear view of how this will fit into the landscape of the field, and will be able to help you avoid the feelings of theoretical inadequacy.