PhD in a less desired field
Obviously we can't answer this question explicitly for you, since it's an opinion.  But I would approach it with this thought process, and maybe you would find it helpful too:

First, I would hold each option up against an outside third option of not doing a PhD at all.  Assuming an average outcome, would be willing to chance an engineering PhD if it meant a lack of funding and job opportunities?  Repeat with the second option - would you be willing to suffer through a social science degree you don't necessarily love, just to have better prospects?  Or would you rather do whatever it is you would do without a PhD?

If both of those answers are that you would rather do the PhD, I think the real thought needs to fall on the second option.  A PhD is a huge, often demoralizing undertaking.  You will almost certainly want to quit at times.  And while most fields, as you said, allow some interdisciplinary flexibility, at least at first you will almost certainly be immersed entirely in the field itself.  Do you enjoy this field enough that it could sustain you through down periods?  

Also, European and US programs are often quite different, in particular in that US PhD programs start right out of undergrad, then do several years of coursework that earns you an incidental Masters, followed by your research.  European programs generally require you to have your Masters coursework done already, then you come in to the program just to do your own research.  Make sure you're familiar with the structure of the programs you're interested in - it's possible that might help narrow your choices down some.

I would also add, especially for the engineering program, that you should talk to some people who have gone through it if you haven't already.  Find out first-hand how good or bad the opportunities were.

Good luck!