What reason makes it preferable to read Birkas haMazon (blessing after meals) from a booklet, but tefilas Amidah with one's eyes closed?
Also what specific reason makes us say Shemoneh Esreh standing, but Birkas haMazon sitting?
The ideal way (Min haMuvhar) to daven Shemoneh Esreh, is to stand facing the wall. The main reason for this is to maximize one's concentration (there are other reasons). When davening in Shul with a minyan, it is usually not possible for each member to daven against the wall. The best thing to do when a wall is unavailable is to close one's eyes during duration of Shemoneh Esreh or to keep one's eyes to be focused directly in a siddur in order for the concentration not disturbed by outside occurences. (Mishna Berura Siman 90, S"K 63 and Kaf haChaim Siman 90:133).