I haven't had that problem with Aldi produce going bad any faster than produce from other stores.
In my neck of the woods (Chicago),the produce prices at Aldi are typically much much less than at the other chain grocery stores (Jewel, Marianos, Trader Joes, or <gasp> Whole Foods.)
The produce at Aldi is typically 30-50% less expensive than the prices at Jewel.
Jewel may occasionally have a sale on meat that is slightly better than Aldi's normal prices (maybe 20 or 30 cents a pound). However, the normal prices for meat at Aldi are generally about half the price of the same cuts of meat at Jewel.
I guess everything is dependent upon what you normally buy. One thing I did notice is, premium cut bacon at Aldi isn't much cheaper than Jewel's sale price (which seems to be a perpetual sale.) Of course if you hit one of the rare times when bacon is not on sale at Jewel, it's way more expensive than at Aldi.
For staples like cereal, flour, sugar, rice, beans, bread, butter, milk, eggs, pasta... Aldi wins every time.