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The phrase 'come across' indicates no direct contact, but 'come upon' does. You can say " Where did you come across this word?" and " Where did you come across such a rare fellow?". You can say "The rain drops fell upon his bald head", but " The rain drops fell across his bald head " seems more inappropriate. Upon indicates a specific direction too, across doesnt.
Spot on. I would also add that the phrases express different levels of "transience" in the contact.
For instance, you would say "I came across that article the other day about..." when referring to something you casually flipped through, had some cursory interest in, considered briefly, and then maybe passed on to someone else or bookmarked for later. However, "I came upon this marvelous find at the yard sale..." is usually reserved for things that surprised, fascinated, captivated, or otherwise motivated you to really do something about them that took longer than a passing glance.
It follows that "come across" is used much more frequently than "come upon." :p