Generally speaking, the flow of globe vales is from down to up. It means the medium will go through from disc downside then out by upside. Globe valves usually adopt compulsory sealed design, so close valve by offer pressure to disc against seat. So if you want to open valve, the globe valve disc must overcome resistance made by stem and packing friction, medium pressure will offer adverse pressure which help open valve. It means you can use less force than closing valve. So the stem diameter should be larger, to avoid stem bending fault.(depends on metal material physical performance of stem ). In recent years, there are more and more valve pressure seal, the medium through upper disc to down disc, so the close valve force is smaller than the open valve force, valve shaft diameter are allowed to be smaller.
But some opinions disagree it, especially for globe valve with larger size (for example, size bigger than DN250), the globe valve is usually adopt valve pressure seal, considering closing valve force, it is easy to reach seal performance. But it should take stabilization of valve into consideration when the valve stem diameter is smaller than seat diameter.
So it is hard to say which flow direction is better, it depends on site situation and project requirement, and valve manufacturer ability and design.