The more positive responsiveness you are feeling is the increase in octane level between the two, Sainsbury’s 97ron and Tesco’s 99ron.
I noticed the same thing (more responsive) when I went from Sainsbury’s super unleaded to Shell V Power (99ron).
Regarding the rattle, it could be down to the engine running smoother. I have read that the 2.0 TFSI engines run smoother with a higher octane drink.