If you are getting interivew invitations from BCG and Bain for the same CV then I would assume it is good enough. Since the McKinsey recruiter will know that you applied last year, I would encourage you to make some updates so that it comes across as a "stronger" CV. 

An EM referral is great, particularly if they are activeliy part of recruiting where the recruiters will value their judgegement. If not, a partner is always marginally better but as you can tell from this forum, referrals are not unusual where it only ensures your CV gets meaingful reading time.

Good luck!

Hi there,

If it has been a year since you last applied, I would sincerely hope that you have some updates to make to your resume! Add anything that has changed over the past year. Importantly, you want to show progress over the past year!

That said, if you got into Bain and BCG interviews earlier, then you should be perfectly safe, especially with an EM referral!

Typically EM referrals dont hold that much sway, however if they are active in recruiting and are willing to push your resume then you have a very good chance of being invited to interview. Especially if they said you have a good resume I would not be too concerned.

Best,

Udayan