Yes and no. I have literally done a spreadsheet on it this week.
I was doing shopping for a scout camp so needed to penny pinch as we were buying in quantity.
Surprisingly on a £200 shop for spag bol for dinner, sandwiches for lunch and cooked / cold breakfast, if you shop at Aldi it would have cost you £2 less than Asda. Its not much.
Thats not the full story though. If you were to split on what was cheaper at Aldi and cheapest at Asda you could save yourself £20 on just shopping at Aldi.
The trick is clearly to either do both if you live somewhere where they are very close or to try and alternate between the two and shop savvy, knowing which products are going to give you a particular saving.
There is a slight cavet to this. I found Asda had more empty spaces on shelves so you couldn't always get the cheapest item and I found Aldi doesn't always stock every product I want.
The really noticeable things you can save on is meat. Sausages and bacon were cheaper at Asda. If you can find the smart price items then you can get savings on some of these items. The noticeable one was orange concerntrate boxes of juice. 55p for smart price. 75p at Aldi. But the smart price range were properly hidden away and not everything seems to come up on their website for the smart price range. And they were often out of stock. Asda also comes up good on some particular items that Aldi only stocked a limited range on. For example if you are happy to switch your Nutella to Asda's own brand version you can save a lot, because Aldi don't have their own line.
On the whole it was much of a muchness on standard products with Asda price matching Aldi on many.
Where Aldi definitely wins is on the detergent and cleaning aisle. I would never go back to brands having switched.
So thats my tip - dont shop exclusively at one supermarket. You can save even more if you dont. Just work out which particular items you buy regularly, work out cheaper at which supermarket.