It depends what you buy. Asda is good for bulk packs, 'big saving events' type promotions, value brands and loss leaders that will sometimes be cheaper for individual items, but you'll find that other things in the shop are more expensive, eg I've just looked at a couple of items that we regularly get in Aldi that are much cheaper than other shops and found that halloumi and chorizo at Asda are £2 and £2.20 where at Aldi, both items are under £1.50. So you'll likely lose the saving by spending more on other items.
The other consideration would be is the quality equivalent. In Aldi, the items is usually equivalent to the main brand, whereas in Asda, the cheapest version might be a value brand, which might be fine, but might also be poorer quality than the Aldi version.
But for things like baby wipes, and many other non perishable things, if you can, stock up where things are cheapest and rotate supermarkets so you only have to buy fresh stuff week to week, and for things like hallomi and chorizo in my example, you don't buy it when you're in Asda, because you bought a few of each when you were in Aldi last week.