Physics doesn't obey a consensus vote, and just saying an unqualified "rigid" doesn't mean anything in the context of machine tools.
Endmill holders have a higher static rigidity, collet holders have a higher dynamic rigidity. Higher static rigidity means less deflection and overall holding force in the endmill. It won't slip, and it will stay straight at low RPMs. Higher dynamic rigidity means less deflection at high speed, and higher vibration damping at all speeds.
The ASPE has a video series, one of which is Dr. George Tlusty. He determined the equations that describe chatter in machine tools, and it's a very robust presentation on how chatter occurs and why. If you're interested in the subject, I recommend finding the two-part presentation and watching it.
I don't have any webpages on this, nor would I trust any, as the quality of information regarding machine tool dynamics is generally piss poor. The places I've seen quality vibration and chatter analysis of toolholders is in journal articles, personal conversations with people who have a doctorate in the subject, and from people who do high speed machining and have done vibration analysis as part of the toolpath. I believe there was a semi-recent issue of Modern Machine Shop that briefly detailed the advantages of collet holders, but I don't subscribe to it and don't know which issue it was.