DaaasYochid, wearing anything with a logo on it explicitly denotes support for that organization, so anyone who wears it for whatever reason is still incorrect in doing so.
anon1m0us, there’s no contest between the two, though organized sports happens to be another topic.
Many yeshivos and camps have taken their students or campers to ball games. As well, many gedolim have proclaimed it’s yehareig ViAl yaavor to join the IDF.
Is it not very obvious which shirt is better to wear?