The battle of the citrus fruits
Though you might have a personal preference, when it comes to the battle of grapefruit vs. orange, it's not that one citrus fruit is better or even necessarily healthier than the other. Really, the difference between grapefruits and oranges is actually quite simple, even though people get still them confused on the regular. Ultimately, the difference between a grapefruit and an orange comes down to the fact that they're two different fruits, though they do belong to the same family of citrus. In fact, as Harold McGee writes in On Food and Cooking, "Currently it’s thought that the common domesticated citrus fruits all derive from just three parents: the citron Citrus medica, the mandarin orange Citrus reticulata, and the pummelo [also spelled 'pomelo'] Citrus grandis."
That's means any citrus fruit you encounter in the supermarket is likely some descendent of or variation on these three original parent citrus fruits—and that includes both grapefruit and the so-called sweet orange with which you're probably familiar. According to a study of the genome of the sweet orange, published in the scientific journal Nature Genetics, the fruit is likely a "hybrid between pummelo and mandarin."
These sweet oranges have been around for centuries, mentioned in ancient Chinese literature. Grapefruit, on the other hand, are kind of the newest citrus fruit on the block. They were only discovered in the Caribbean in the 18th century, and they are likely an accidental hybrid of pummelo with sweet orange.
The way grapefruit grow on a tree is also slightly different than the way oranges grow, and that's another easy way to tell them apart if you're lucky enough to be looking at citrus fruit on trees, of course. Grapefruit get their name in part because they grow in clusters, almost like grapes on a vine. (Though some experts think this is kind of bogus. Etymologist John Ciardi told National Public Radio that it's likely a mixed word. As Julia Davis explains in Mental Floss, "The pomelo’s scientific name is citrus maxima, which can reasonably be translated as 'great-fruit,' a reference to both the pomelo and the fruit’s size," and that phrase was later corrupted to "grapefruit.")
So what's the best way to tell a grapefruit from an orange if you're just hypothetically handed two citrus fruits? Grapefruits tend to be larger and heavier than sweet oranges (though, to be fair, there are also different types of grapefruit out there). And if you're still in doubt, just peel that fruit. In general, a grapefruit has a pink or red flesh while a sweet orange is, well, orange. And really, either will taste just fine.