The Big 12, when formed, had the following members:
AAU Institutions
Colorado
Iowa State (no longer AAU)
Kansas
Missouri
Nebraska (no longer AAU)
Texas
Texas A&M
Non-AAU Institutions
Baylor
Kansas State
Oklahoma
Oklahoma State
Texas Tech
The current Big 12 once it loses UT and OU will only have a single AAU member
Worse, in terms of graduate research intensity & funding (Carnegie Classification), every non-AAU was R1 (the top level - Doctoral universities with very high research activity). It's a high standard, but not that high of a hurdle - about 130 US schools meet that standard. It's kind of the minimum for CU to consider a school to be a peer university.
The new Big 12, beyond having only 1 AAU member, has the following R2 schools: BYU and TCU.
Comparatively, the 10 members of the Pac-12 are all R1 and the following are AAU members:
Arizona
Cal
Colorado
Oregon
Stanford
Utah
Washington
FWIW, this has been a major issue with expanding the Pac-12. The only FBS football AAUs not in a major conference and somewhat "West" are Rice and Tulane.
The Western non-AAU R1s not in a major conference are CSU, Hawaii, LA-Lafayette, Nevada, New Mexico, North Texas, UNLV, UTEP, UTSA and Utah State.
SDSU is now being considered because of desperation. It has had success and is in the vital So Cal market. They're R2 and there's a ton of political stuff about the U Cal vs Cal State systems. Cal States are limited by statute on doctoral programs. Maybe that changes now or Cal accepts the prestige hit of sharing a conference with an R2. Something has to give or they won't get an invite.
SMU is solely about desperation and the Dallas market. Not just R2, but also religious affiliation. Not a peer institution, so this would be hard to swallow for many Pac-12 members.
My guess is that they'll follow the money as the top priority. Conference will stay at 10 if it's close. They'll swallow hard and go to 12 if it makes a big difference on revenue.
The move which should have been made as soon an UT & OU announced for the SEC would have been UH, TTU, KU and UNLV to create a Pac-16 and to renegotiate its media deal early. But we missed the boat.
Edit: The big one for prestige is the Shanghai Ranking of world universities (ARWU). Being in the Top 100 is something the B1G and Pac-12 always highlighted.
Cal, Stanford, USC, UCLA, Colorado and Washington are all Top 100.