Hard new ideas VS Hard technical ideas?
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.