Actually pretty much every midi tracker program (which Logic is even though it also does notation) use delta-time units, of which 3840 per quarter note is pretty standard practice.
Sibelius & Finale are only notation editors. But notation editors might even internally represent the midi event times using 3840 delta-time units even though they deliberately hide that from the end user, for good reason because their user base is musicans who play written sheet music instead of dealing with midi. I don't know that for sure about Sibelius & Finale since their code is closed, but the open source MuseScore editor does use 3840. [1]
Hold on while I break out a calculator to operate my computer. As a former sound engineer I have to tell you nobody liked Logic, they tolerated it as the affordable alternative to Pro Tools until other tools came along. People appreciated its reliability and depth but not the UX.
Though maybe I was just too stubborn to re-input things in different software for each purpose. Needless to say, on the coding side, I was very excited when Node.js was first released!
Apple's (formerly emagic's) Logic software actually made this visible to the user, using 3840 delta-time units per quarter note and presenting an Event List interface [1] where you could edit integers for offset and length directly. As opposed to other WYSIWIG notation software like Finale and Sibelius, it felt like Logic was hiding nothing from you; you could be sure that everything you saw and heard was rendered declaratively from the same underlying data. Moreover, if you were ever having trouble zooming/subdividing the drag-and-drop user interface for whatever crazy triplet sequence you wanted, you could just break out a calculator and specify exactly what you want, knowing that you wouldn't be "fuzzing" anything by typing in a rounded decimal number.
(It's a good lesson for us as developers - while it can be extra work to build an interface that doesn't hide complexity, professional users will often figure out how to use this to work around other shortcomings in your interface, buying you time to fix them the right way. It's just a matter of finding the right abstractions - representing time as integers is just one example.)
[0] https://www.csie.ntu.edu.tw/~r92092/ref/midi/
[1] https://support.apple.com/kb/PH13096?locale=en_US&viewlocale...