Is there a formal word to describe someone who sees not just the particulars, but also the bigger picture?
I have never come across a term which explicitly means "seeing not just particulars, but also the whole", without any other connotations. There are several words which come close to that concept, though.
Perceptive, perspicacious, insightful, or sagacious could be a good fit for what you're looking for.
Sharp or shrewd imply quick grasping of a situation.
Clairvoyant means that one can see beyond what the normal human senses can register, though it is often used in a context of mysticism. Not always.
Holistic, suggested by @brachomonacho, can be close, but it has some connotations that you might not want. Among other things, it often means complete or whole. See the thesaurus.com entry.
A person with a broad general knowledge, especially one with more than superficial knowledge in several areas and the ability to combine ideas from diverse fields.
Reference is this wiktionary page.
There are several phrases, particularly common in "biz-speak," that refer directly to this quality. To wit:
"He's a big-picture kind of guy. He sees things above the clouds. He can give you the elevator view."
Also, a big +1 to Ivo Rossi's contribution of "generalist," which usually means someone who isn't possessed of a great deal of granular information, but is good at seeing how various items relate to each other in a macro-level way.
Visionary is the word.