With the whiteboard test, as a candidate, I know that when my hour is over, its done. Plus, I can get feedback during my whiteboard session to know if I'm on the right track, I can ask questions and get guidance on where to concentrate my efforts. With take home projects, I've woken up in the middle of the night and thought, "Wait, I know this is a full stack position, and they said that the UX just needs to be functional, but maybe my CSS knowledge is too old, and there's a better/newer way of doing the styles. I should really spend all night researching this, wait, BOM?! I should convert over to that, I don't want the front eng engineer reviewing this code and saying, OMG, this is so old, NOHIRE!"
EDIT:
Also, take home challenges are probably very discriminatory towards older candidates with families. So maybe just as subtle way of age discrimination?