BYU and Utah should no more be counted towards the MWC than UNLV (a former WCC member who departed for the Big West for Football reasons while Tark was coach) should be counted towards the WCC. Utah's history is naturally going to be counted by the Pac-12, just as TCU's football history is going to be claimed by the Big 12.

A brief comparison of today's MWC vs. today's WCC (which makes sense, because that's reality):

For the record, in the pre 1954 era, the WCC is certainly stronger head to head (2 NIT titles--USF and BYU--and a Final 4 by Santa Clara) outweigh the 1943 NCAA title by Wyoming. 1954 is used because that's the year most basketball historians consider the first year of the "modern" era, and the first year the NCAA Tournament is considered to have permanently become the primary and only National Championship awarding tournament (for a brief example, in 1953 #2 Seton Hall won the NIT, which they chose to play in for, in part, because of race reasons).

National Championships and Final 4's:

West Coast Conference-4
1955 San Francisco (champ)
1956 San Francisco (champ)
1957 San Francisco
2017 Gonzaga (runner up)

Mountain West-4
1977 UNLV
1987 UNLV
1990 UNLV (champ)
1991 UNLV

Elite 8's (not counting Final 4's):

West Coast Conference-13
1954 Santa Clara
1959 Saint Mary's
1960 Santa Clara
1964 San Francisco
1965 San Francisco
1967 Pacific
1969 Santa Clara
1973 San Francisco
1974 San Francisco
1981 BYU
1990 Loyola Marymount
1999 Gonzaga
2015 Gonzaga

Mountain West-3
1969 Colorado State
1970 Utah State
1989 UNLV

For recency, total Sweet 16's (or beyond) over the last 20 years:

West Coast Conference-3 schools combined for 10

1999 Gonzaga Elite Eight
2000 Gonzaga Sweet 16
2001 Gonzaga Sweet 16
2006 Gonzaga Sweet 16
2009 Gonzaga Sweet 16
2010 Saint Mary's Sweet 16
2011 BYU Sweet 16
2015 Gonzaga Elite Eight
2016 Gonzaga Sweet 16
2017 Gonzaga Final Four

Mountain West-3 schools combined for 4

2004 Nevada Sweet 16
2007 UNLV Sweet 16
2011 San Diego State Sweet 16
2015 San Diego State Sweet 16

Total NCAA win count (even including pre-1954, which benefits the MWC):

West Coast Conference

96 (9 of 10 WCC schools have at least one NCAA win)

Divided by 10 WCC schools equals 9.6 NCAA tournament wins per WCC school.

Mountain West

72 (8 of 11 MWC schools have at least one NCAA win)

Divided by 11 MWC schools equals 6.5 NCAA tournament wins per school.

National Player of the year Awards and National scoring leaders:

West Coast Conference (4 National POY's):

1956 Bill Russell-USF (National consensus POY)
1961 Frank Burgess-Gonzaga (National scoring leader)
1973 Bird Averitt-Pepperdine (National scoring leader)
1981 Danny Ainge-BYU (Co-POY)
1989 Hank Gathers-Loyola Marymount (National scoring leader. Lead nation in both scoring and rebounding)
1990 Bo Kimble-Loyola Marymount (National scoring leader)
2006 Adam Morrison-Gonzaga (National scoring leader and National Co-POY)
2011 Jimmer Fredette-BYU (National scoring leader and National consensus POY)

Mountain West (1 National POY):

1991 Larry Johnson-UNLV (Co-POY)
2000 Courtney Alexander-Fresno State (National scoring leader)
2003 Ruben Douglas-New Mexico (National scoring leader)

Judging by postseason success (the ultimate metric, and the end-goal of every program and conference), it's impossible to judge the WCC anything other than significantly superior in history to the MWC both in the short term and long term.