I don't have an Aldi near me, so can't compare. But my Lidl shop is about 60% of what it would be in Tesco, so it is well worth going there for me.
To give you an idea:
I buy meat,veg,fruit,tins, dairy,sandwich stuff, pasta, bread and cereals there, plus all laundry and cleaning products . I buy lidl's own staple brands which ime are just as good as any of the supermarkets but much cheaper
But there are things I can't get so I always end up doing a top in Sainsburys for things like fresh ginger, harissa, thai green curry paste, fresh fish (only do a few frozen things like prawns), oxtail and game etc
This year they have started doing coconut milk and chickpeas at my local Lidl which were always on my top up list, so hopefully eventually they'll sell everything!
The only real problem I have is their own dog meat is not very nice and the only branded versions they sell such as Bakers and Butchers are both owned by Nestle, who we boycott, so I have to buy dog food tins a hundred at a go and get it delivered!
It really is a LOT cheaper for the basics, though.