Both are rated and ranked as 'Very Good' colleges for management studies by Careers360.

That is both are rated as AAAA.

You can check the reviews for both here:

SIBM

IRMA

Also IRMA has its flagship programme in Post Graduate Diploma in Rural Management (PGDRM) so it also depends in which specialization you want to go in for management course.

SIBM has its specialization in MBA (INNOVATION & ENTREPRENEURSHIP).

So accordingly you have to decide which course you are interested in and then colleges later.

Also for admissions in IRMA, IRMA will use CAT / XAT  scores for admission to Post Graduate Diploma in Rural Management.

And SIBM Pune will take through SNAP entrance.

Applications for CAT has already started.

All the best.