I'm not convinced by double degrees.
In the same time frame you could have a masters too or be started into a PhD programme. The depth of your knowledge will be greater that way and give you better exposure to whichever industry when it comes to job seeking.
Perhaps any US IISer may like to comment, as both of your chosen paths have a high chance of work State-side, and when I graduated, the companies were looking for Masters level entry candidates. That was 25 years ago, so things may well be very different!
But which ever way you chose, stick by your decision and have fun. It is a long haul, but very satisfying
