What a fun question! Yes, the story has been going around for more than the last decade - take this as an example (ironically, from a book entitled "Unreliable Sources"). Princip was also standing outside a local food shop on Franz Joseph Street at the time, which may give further credence to the claim. I'm afraid, however, that the story of Gavrilo Princip eating a sandwich prior to the assassination is most likely an invented story, with no actual historical basis. Here's why.

Firstly, before hitting the books, it's worth looking at some of the articles claiming to debunk this myth online. This article raises a few questions:

• Isn't it a bit of a convenient story, that had he not gone to eat that sandwich he wouldn't have been standing in the right place to assassinate the Archduke, and perhaps have not set in motion the chain of events leading to war?

• The murder took place at just before 11 in the morning. Isn't this a little early for lunch?

• Even if he was eating, was a sandwich a common option for a Serb eating in Sarajevo in 1914?

None of these questions actually tell us much, of course. Plenty of seemingly ridiculous stories can be true. Plenty of people eat lunch at different times. On the third point, I'd appreciate anyone with a knowledge of Serbian historical cuisine to confirm/deny that, but until then we must assume that it was possible that a café in Serbia could have sold a sandwich (edit: see replies to this comment).

So onto the books. It is true that Princip waited outside a local café called Schiller's, on the corner of Appel Quay and Franz Joseph Street, as reported in his trial (Dedijer, p.323). Reputable historians including Christopher Clark have also reported this but make no mention of Princip eating at all:

"This was Gavrilo Princip's moment. He had positioned himself in front of a shop on the right side of Franz Joseph Street and he caught up with the car as it slowed almost to a stop" (Clark, Chapter 7).

It was clearly not a coincidence; Princip did not simply step outside of a delicatessen eating a sandwich and just happen to spot the Archduke. After all, Princip's position was still on the route the Archduke was originally planning to take. But nonetheless just because Clark and other historians omit what was really a minor (if slightly interesting) facet, doesn't mean it wasn't true. Perhaps historians like Clark saw Princip eating a sandwich as an unimportant and trivial detail?

The real giveaway is that there isn't a single mention of Princip eating a sandwich prior to the turn of the millenium. It's not in Albertini, or Clark, or Dedijer. A dated search doesn't turn up any results either. So what was the origin of this story? Here, the article previously linked does a good job. It appears to originate from a novel by Jô Soares entitled Twelve Fingers: Biography of an Anarchist, about a would-be assassin who attempts and fails to murder the Archduke Franz Ferdinand. Here's the relevant quote, beginning with the main character, Dimitri Borja Korozec:

"Gavrilo! It's been such a long time! What are you doing here?"

“I’m eating a sandwich”

“I can tell that. Don’t treat me like a child"

They fall silent, while Gavrilo finishes his sandwich and takes a grimy kerchief from his pocket to wipe his hands. When he opens his coat to put away the kerchief, Dimitri sees a Browning pistol tucked into the waistband...

This book, originally in Portuguese and translated to English, was published in 2001 and is a work of fiction and is the first piece I can find which claims that Princip was eating a sandwich. From here, it seems to have been popularised by a documentary television series on BBC Two entitled "Days That Shook the World", airing in 2003. The programme in question was from season 1, episode two, the episode called "The Assassination of Franz Ferdinand/The Death of Adolf Hitler". This episode was aired on September 17th, 2003. From the smithsonian magazine, the narrator allegedly claims:

“Gavrilo Princip has just eaten a sandwich, and is now standing outside Schiller’s delicatessen … when suddenly the Archduke’s car happens to turn into Franz Joseph Street. Completely by chance, fate has brought the assassin and his target within 10 feet of each other.”

Poor documentary fact checking! This is most likely where the widespread proliferation of the myth began, as the BBC documentary was broadcast worldwide and so helped to popularise this piece of fiction.

Hopefully, this myth has been debunked as best as possible. It appears in no history books that I can find pre-2001, and seems to have been most popular online and in the aforementioned BBC documentary, as well as some semi-historical books. The origin of the myth is most likely from the Brazilian work of fiction, Twelve Fingers, and has no basis in historical fact. So, sadly, I can't tell you what kind of sandwich Gavrilo Princip was eating at the time because he most likely was not eating one at all.

Sources:

• The basis of my argument came from here.

• Simpson, John: Unreliable Sources: How the Twentieth Century Was Reported (2010).

• Clark, Christopher: The Sleepwalkers: How Europe Went to War in 1914 (2013).

• Albertini, Luigi: Origins of the War of 1914 (1953).

• Dedijer, Vladimir: The Road to Sarajevo (1996).

Odds are that Princep wasn't eating a sandwich at all. None of the original sources mention a sandwich... in fact no source seems to mention it prior to the early 2000s. Apparently the sandwich story also only seems to appear in English language versions of the assassination. A Smithsonian writer investigated the story and has tentatively identified the British TV show Days That Shook The World as the point that created the sandwich story.

This makes sense as sandwiches are not typical Serbian food, and were even less so in 1914. No eyewitnesses place Princip inside the Deli, nor do any of them mention him holding any food, let alone a sandwich. All witnesses place him outside the deli, no one mentions him entering the shop. As the assassination happened before 11am, it'd be a bit early for lunch anyway.

In all likelyhood Princip was there, simply because he hoped for another chance to shoot the Archduke. The spot he was hanging out was along the original parade route. It was also a major thoroughfare. The Latin bridge was one of a few limited ways across the Miljacka River. Far from coincidence, it seems like Princip intentionally staked out one of the places the Archduke was likely to appear.

Thanks /u/frederfred1 and /u/QuickSpore for the wonderful and thought out answers.