does it matter if one's from an assistant (new) professor who knows you well because he was more approachable than the other egoistic ones you find at a top-3 program?
According to my own professors, yes, it does matter who your letter is from. I was in a similar boat, actually. I had two letters from senior faculty, and the most obvious third one would have come from the new assistant professor who supervised my senior thesis. However, my senior references cautioned me against that. Instead, they suggested that I should get the substance of my letter written by the assistant professor, and have that incorporated into a letter written and signed by a benevolent professor who was more connected. I am very lucky that that worked out for me.
If that's not an option for you, you are probably still better off with a meaningful letter from a young professor than an empty letter from an accomplished one.