Part 141 or 61?
In my experience if you are trying to get hired as an instructor at a part 141 school then it definitely helps to be a graduate from the same program. However one of the main differences in part 61 versus part 141 is that the main benefit of part 141 is to trim flight hours.
It takes more flight time to reach the experience level to get the commercial license. As a result the 141 graduate has to bridge that gap in flight time when looking for a job therefore 141 can be a disadvantage.
Skyhigh