Since my friend is an alumnus of IIIT Allahabad, she will be well suited to talk about the faculty of the institute.
All the teaching staff of IIIT Allahabad is Ph.D. holders from institutes that are reputed, for example, IIT Bombay, IIT Kharagpur, IIT Kanpur, etc. Some of them have received their Ph.D. from institutes like the University of Reading, UK. So it goes without saying that the faculty members have expertise in their respective areas of teaching.
The teaching style of the faculty is the same as that of other institutes like the IITs and/or IISc. They teach during the class. If you have doubts, you can ask the faculty and they will be very happy to resolve the same. They are very supportive.
Don’t make faculty a major deciding factor for choosing an institute. Both IIIT Allahabad and MNNIT are reputed institutes in the field of IT.