I think you need a third choice; 'no difference'.
Perhaps with CAM it is different, but I hand code regularly on both and find them more or less the same. It is sometimes difficult to switch quickly from one to the other and remember that lathe incremental uses U and W while the mill is G91. Also I sometimes get feeds mixed up, but fortunately if I tell the lathe to feed at 50.0 and it is using IPR it alarms rather than crashing and on the mill a feed of 0.005 is just very slow.
The difference I find between the two machines is running them in MDI or using handle jog; to me it is much easier on the mill. Also when I just want to drill and tap a single hole in something it is often much easier on the mill to set up the tools.
An open mind is a virtue...so long as all the common sense has not leaked out.