There is a big difference between 121 and 135. 121 operators require longer training footprints than 135 operators. That means there is less "hand holding." A 135 company will send you to a 142 training center where they will teach you the checkride, and nothing else. After that, you are sent to the line with no training wheels. Unlike 121 IOE, you won't get easy trips to help transition from the sim to the real world. Your first day could be a full 14 hour day with minimum turns doing special approaches into mountainous airports. That would never happen at an airline.

Part 135 companies generally have higher minimums because they need pilots who already know the basics of operating a turbine powered aircraft for revenue. Ideally, they want someone who has worked at another 135 or 121 company before.