How bad would it be to graduate with a thesis not able to show positive results?
While your advisor can probably help, don't misunderstand the purpose and process of research. It isn't making some unsupported claim at the beginning and then "proving" (dammit) that your claim was accurate. Research is a reach into the unknown. The answers you get depend on what is, not on what you want them to be. 

You are actually seeking knowledge (truth), not verification. If the results of your research disprove your original hypothesis that is still a valid result. 

If your "new" technique isn't actually better than the old, then it is useful (maybe vital) to know that. 

In an ideal world you should be able to write that up. We hypothesized X. We used process Y to explore it. We found no evidence that X is true. That is still knowledge. 

Hopefully, however, your advisor has such a view. And hopefully your process Y was sufficiently sophisticated that you haven't fallen in to easy errors. 

If every hypothesis came up with positive (supporting) results, we wouldn't be working very hard and only making trivial initial hypotheses. 

But, start out with "what is true here" rather than "this is true and I'll beat it until it yields". That leads to propaganda and isn't research. It is often the basis of misconduct. Tobacco and pesticide "research" too often fall into such errors. 

So, it isn't "bad" at all if you reach truth.