When we moved I changed from shopping in Tesco and Asda to Morrisons and Aldi. I have to say that most of our favourites are in Aldi, home brand. I prefer their bacon (the cheap stuff), butter (Welsh salted), Brie, fresh meat (British) and their posh pasta is the biz. Staples like olive oil, the odd tin of beans, tinned tomatoes, pasta etc are probably on a par with other supermarkets because of price matching, but I go to Aldi for the stuff I like.
We have to go to Morrisons for John Smiths (Phill drinks it), Tanqueray 0% and Eisberg & Freixenet 0% wines.