Own brands
It much depends on where it is made (i.e. which manufacturer is making it).
I have found Lidl's Formil Bio powder (in the green box), to give very good cleaning.
A friend commented on how white my white towels were! But he uses liquitabs and has mostly coloured laundry, that gets washed together. Ultimately in his case, any white items will end up off-white.
Having checked the Lidl ingredients, there appears to be six enzymes in the detergent (protease, lipase, pectate lyase, and three glycosidases).
Tesco Bio seemed to clean okay too, but I wasn't particularly taken by its perfume.
My mum tried the Home Bargains "Ultra" Bio (apparently made by Robert McBride detergents). It didn't clean properly, it foamed quite badly in her Bosch machine, and my dad became allergic to it. So, not exactly a resounding success!
I was in Semi-Chem recently and scanned an eye over their detergents. They had a cheap brand called something like "Essential Rituals", with some kind of flowery fragrance. The packet was a small, 10 wash size, but weighed a ton, compared to the similar sized packet of Ariel! I looked at the ingredient list, and it stated that it contained "metasilicate". Metasilicate was used in the old-style, corrosive dishwasher powders.
As for dishwasher detergents, Lidl's gives good results.
I had purchased a box of the Persil dishwasher tablets (made by McBride detergents) for my mum, but they seem to be leaving a fine, chalky, powdery coating over the stainless steel lining of the dishwasher. I noticed it by the way the light was not being reflected off the open dishwasher door. I won't be buying those again.