Look at all of the Flybe Dash and EMB pilots who are getting no love in the Gulf because they don't have the types or experience needed to get noticed. Sure, no problem if you never want to go to the Gulf, but the point is that in Europe, having the right type ratings and sufficient experience on type can bring you to the head of the queue. It's a fact of life.
Everyone wants PIC time, but you should consider the job that will advance your career faster unless you want to slow it down. Look at the recent Jet2 ads - they are looking for people with 737 experience. I say the 737 choice is a no brainer.
Good luck.