Mostly I'm immersed in the details and I have a lot of difficulty in switching my attention to the Big Picture, but once I'm in BP land I'm fairly comfortable with it. Really a Big Picture is little different to a Small Picture......just a matter of focussing on another level, just like moving onto the next picture in an art gallery, though the brain needs a bit of time to realign itself. I don't think there's anything intrinsically hard or Aspie-unfriendly about it.
I suppose most of us use the Big Picture whenever we use a computer - unless it's your special interest, you probably just use the graphical interface without trying to figure out what's happening to the 0s and 1s in the RAM......though I do recall that when I first started learning about computers, I had trouble overcoming my curiosity about exactly how they worked - and when I failed to suss it all out on that level, I had a very bad feeling that my understanding of computers was deeply flawed. But I got over it. I still don't know how my computer works, but I know how to work it, and that's all I need to know. Life's too short to trace out every stupid detail.
I do have a penchant for the details and am generally more comfortable in that "head space," so I have some tendency to drift back to detail, but it's not insurmountable, and it only takes somebody to remind me that there's a bigger picture I'm missing, for me to appreciate that I need to look up. It's harder to get it right when I'm stressed out or tired, and then I can end up lavishing care and attention on the tiniest, most insignificant details. I think I also do that if I "let myself go," so I suspect it's a natural tendency of mine to be a "detail thinker," and that I only stay out of the trap by routinely applying corrective pressure to my thinking style. A while back I was looking back at my life and I was rather dismayed at how much time I'd wasted on details when a quick glance at the Big Picture would have shown me much easier ways of getting what I wanted. So I guess I took the point and am now rather more careful about locking myself away for years trying to re-invent the wheel.