This would depend on the print size. I would think you'd be able to screen print much finer detail that can be achieved with vinyl but i'm completely assuming, as i have never worked with vinyl before. :/
Most fonts would be ok to screen. You will need a higher mesh count to hold the detail when burning. With screen printing you can add an outline or stroke to the font to make it thicker. With vinyl, using Corel, often times when I add the outline I convert the outline to curves and then weld the outline and fill together to give me the thicker font.
Once you start getting to a 1/8 - 1/4 an inch vinyl almost becomes impossible. Just did some small fonts with capital A and weeding the top of the A was a PITA. Find the tiny little piece to weed out was not fun.
Screen print is defintely much better at these smaller sizes.
With all the lines going through the letters, you will definitely have problems with smaller font sizes especially if you are using a white ink or something that is thicker. If the letters are bigger, it shouldn't be a problem but I would still use a bit higher mesh count.
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