Right now the Sun Bowl trumps the LV Bowl. History, stadium, attendance, etc. When the new stadium becomes a reality, the LV Bowl will trump the Sun Bowl, no getting around it. Stadium, money, prime destination, etc.
UTEP needs to work with the Sun Bowl people (all are El Pasoans) and CBS, the long time media partner with the Sun Bowl, and with the ACC and MWC to have the MWC champ (when not in the Access Bowl) vs an ACC team. UTEP's angle would be membership in the MWC, not so UTEP can play in the Sun Bowl but because it needs some leverage to get into the MWC since it is full right now.
UTEP normally has a solid basketball program and when (seldom) successful in football has very good attendance in football as well.