You are not going to get a quantitative definition of comparable.
Comparable has so many nuances that it can be anything you want it to be, and anything your reader reads into it. In your sentence
It is not expected that the power-effectiveness will equal the
effectiveness of dedicated hardware, but it is hoped that it can be
Replace "....it is hoped that it can be comparable" with an unambiguous, quantitative statement.
In one of your comments, you say: "The power consumption of my design is within 2.5 times the power consumption of the dedicated module.... "within" because it varies with frequency, 2.5x is the worst case."
Thus, I suggest: "The power consumption of my design varies with frequency, and, at worst, is 2.5 times the power consumption of dedicated hardware."
You have summarized concisely and without ambiguity. Forget "comparable" and "order of magnitude", which you are going to have to explain later anyway.
Edit in response to Hida's comments about expectations
I suggest that you present your expectations in terms of "acceptable", rather than "comparable". You decided to build this piece of equipment instead of buying it because...why? It was cheaper? Possibly by building it yourself you improved some key aspect of its performance at the expense of other aspects you didn't care about? If so, try something like: "The equipment that I build was much less expensive than off-the-shelf equipment would have been; it [did whatever it did] as well as (better than? nearly as good as ?) the commercial product would have, although with an increase in power consumption, which could be held to an acceptable level."
You are going to explain all this quantitatively later. Acceptable conveys the message that you had quantitative criteria, which you met. Comparable doesn't have that connotation, to me, anyway. You define what is acceptable; anyone can define what is comparable.