I have experience of children doing both these assessments, and of children going through SAHS and HABS reception currently. SAHS expects them to know all their letters and sounds and numbers and recognise them, plus cut a circle out with scissors, listen to a story and say what might happen next!
Habs, interestingly, does not expect them to know their letters etc, but they all do, and come from quite formal nurseries and preschools and the children all seem to speak at least 2 if not 3 languages in the current reception class! They are expected to be sociable and work in a group as well as show independence and confidence.
I was surprised how Habs really stick to the Early Years Foundation stage in reception ( rainbows) no homework, books etc in the first term and letters start in the 2nd term. The children are encouraged to explore and be confident in the outside world, lots of lovely outdoor play and the writing etc seems to suddenly emerge from all those experiences.
SAHS have opted out of EYFS and it is far more intensive, words from the start, books to read, homework and they pile it on very quickly, more so than the senior school!
I didn't think my daughter was a HABs child ( she did get in ) and still don't, she loved SAHS, so look at the school to suit your child's personality.