It's hard to find a teacher that can address all of the things one is concerned about as a pianist. Inevitably, some teachers are more focused on, or better equipped to focus on, certain things. While one teacher may be excellent at addressing touch, one might be better at helping to develop one's sense of lyricism or phrasing. This is one of the main reasons I believe it is so important to study with a few different teachers. It may not be possible for everyone, but it is inevitable if one is on the track to be a professional musician whether via academic means (BM/BA > MM > DMA) or otherwise. My freshman year as a BM I developed a great relationship with my teacher and I learned quite a lot from him. He left my school to move on to more promising opportunities, and though I was greatly saddened by it, a new teacher opened up other facets of learning that I had yet to experience.
But to stay on topic, nice/strict are not mutually exclusive of each other. If your experience with these teachers is "either/or" then maybe you should listen to what those "strict" teachers are telling you and take it to heart. If you'd listen, then they wouldn't have to tell you repeatedly, thereby making them more "tolerable" for you. If your "nice" teacher DOESN'T enforce all of the above that you listed, then they're not really a teacher worth having are they?