Chances for MM vs BB in Investment Banking

It's the fun answer of it depends.

You've provided no information so I will shoot out some:

• BB's and other large banks are typically the most likely to screen using your school and demographic background. Since there are so many applicants, I have typically seen that BB's will only go to certain schools for IBD positions or will seek diversity candidates from outside ("non-target") schools. That being said, networking still can always help
• MM banks that are larger will follow the trend of going to certain schools - ie Jefferies, HL, etc typically only recruit from certain schools but MM banks are typically more open if you show a history of working hard regardless of what school you come from. Smaller MM banks really require more networking to get in but are more agnostic of where you went to school / your demographic background. This is because they simply need people who are good at the work so they are typically more open.

TLDR; Bigger banks (whether BB or MM) are more likely to use demographics and educational background. However, networking can always help get you in. Money here matters less for difficulty

MM don't pay less. Most banks pay street.

Kind of anecdotal but Jefferies's energy group has often been known be one of the highest paying groups on the street with analyst 1s crossing 200 even before the pay bumps. That said, it is also one of the sweatiest groups

Not true that BB pays more than MM. If anything, it is more likely the other way around, if you're comparing BBs to global, full-service MMs like William Blair, Piper Sandler, etc.. MMs have to pay more to attract and retain talent in more often tier 2 or 3 cities for a "less reputable" firm name. Also, MM is more active, including in down markets (MM M&A activity is more resilient to economic changes than the market for BB-sized M&A deals) so pay and job security is likely less variable/volatile/risky.