How should a social scientist deal with envy of disciplines that are more quantitatively rigorous?
Speaking as one outside of the social sciences whose work has been strongly influenced by readings from social science, I think it may be clearer if you tease apart three concepts that are often conflated: rigor, funding, and importance:


The mathematical or analytical rigor of a subject makes it more difficult for outsiders to understand or hold an opinion on, and inaccessibility can make things seem more important, but all it really shows is that it is hard to understand.  
The amount of money thrown at a subject is another easy proxy for importance, but all that really shows is either popularity or market structure.


Social sciences actually deal with a lot of the really hard problems of society, the things that we all struggle with and don't know how to deal with well, like injustice and politics and social conflict.  We in the hard sciences and engineering like to pretend that we can solve these problems by the injection of new technologies, but all we can really do is create disruptions that destabilize the current order, following which society may become either more inclusive (e.g., the creation of the internet) or more exploitative (e.g., the creation of QoS protocols, leading to the current battle over net neutrality).

Social sciences are further challenged by problems of instrumentation (most of what they care about is really hard or inappropriate to measure), replicability (many phenomena are large enough or long enough duration that we've only got one or a few data points), and experimental controls (many interesting experiments cannot be performed because they would be horrifyingly unethical, e.g., isolating populations from the rest of society).

And yet... and yet I think the social sciences produce some of the most important work for us as humanity, because the work done therein is part of the reason that the arc of the moral universe bends toward justice.

So I think it's OK for a social scientist to envy the accessibility of data for people who only need to build a multi-billion dollar machine in order to do their research.  But don't envy them their field: your problems are just as important as theirs.