Meh. They're all just different colour supermarkets. Stocking eccentricities aside, most of what they sell is the same. Of the own-brand stuff, some are good and some are bad.
Personally, I use Aldi because it's close and good at fresh meat and generic non-food items, and you can occasionally pick up a bargain on cycling gloves, tools or thermal underwear. Sainsbury's is further away but has Lactofree products, decent veg, bigger packs of decent bogroll, proper chocolate and less wastefully sized packets of cheese. Tesco is a decent ride away up an annoying hill and has horrid smoker-infested bike parking, but has the best rice and own-brand pure orange juice, so I do a trailer mission every several weeks. There's a decent sized Asda not too far away that I never use because the logical cycling route, while flat, involves far too much Sustrans path shenanigans. The nearest Morrisons is the wrong side of the Col de Priory Road, protected on all sides by some of Birmingham's finest motorists, and generally quite expensive.
Distress purchases can be made at one of the smaller Sainsbury's or two Tescos within a few hundred metres walk. They're often useful (especially as someone pointed out the utility of self-humiliation checkouts for disposal of excess change), but more expensive.