NOTE: I fly in CANADA. Also, the question is specific to light aircraft like a C172.
It is known that the (standard) glideslope flown in an ILS approach is 3o to the T point. However, that is not the case for a visual approach. Some basic high school math tells us that an aircraft 1 NM away from the T point on a 3o ILS glidepath would be at 319 FT AGL, whereas I'm supposed to be at around 600 FT AGL (or, "ideally" 500' AGL- the same as when turning crosswind) when turning on (approximately) a 1 NM final from base in a VFR traffic pattern- making my "glideslope" about 5.6o (or min. 4.7o if at 500').
What is the reason for this difference in glideslope between a visual and ILS approach?
An answer at this PPRuNe post says that the angle was chosen as it supposedly worked well for the flight computer to be able to AUTO LAND the aircraft. However, that begs the question: why enforce this even in a CAT 1 ILS approach where the pilot takes manual (and visual too, perhaps?) control way above the T point?
 For the sake of simplicity, I use "T point" to interchangeably refer to the aiming point AND the touchdown point.
 I vaguely recall reading somewhere that the term "glideslope" only makes sense in the context of ILS but I use it to refer to my visual glidepath angle anyway again for the sake of simplicity.