As you have easy access to companies in the EU, I'd go that way. However, there's merit in getting both licences.
While the degree is "free" - there are costs and it also costs time. However, you are young and so you have time.
The Integrated v Modular - I'll leave for others. My personal thoughts are that if you're not on a tagged scheme (That is, a conditional offer from an employer), then Integrated can be extremely expensive for what is effectively the same licence. Also, if there's a downturn etc (and that can happen) then you'll be "dumped" onto the market with a rapidly "fading" instrument rating. However, that is my opinion only.
Do you want to do the degree? What employment prospects do you have after graduation? Can you work post study and earn a good amount of money to fund your training and thus, minimise your exposure to debt?
Does the degree offer work placement? If not, then a PPL while on holidays is feasible. ATPL subjects + engineering degree = massive workload!
Work experience will offer insights. More the merrier.
Good luck.