I would say that it is the same in informal correspondence, but if you are writing a formal letter, it's probably best to avoid it.
24/7 (or 24-7 or twenty-four seven) is given the label "slang" here in a couple of dictionaries at Dictionary.com: Dictionary.com Unabridged, based on the Random House Dictionary, and The American Heritage Dictionary of the English Language, 4th ed. The Oxford English Dictionary, which has an entry for 24-7, but shows the other two spellings as well, labels it "colloq. (orig. and chiefly U.S.)."
Google Books shows examples of twenty-four hours a day, seven days a week; 24 hours a day, seven days a week; and 24 hours a day, 7 days a week. If I were to use it in a formal letter, I think I'd choose the version which spells out the numbers.
It also shows examples of 24/7, of course, but I would still suggest avoiding it in formal correspondence.