HEB used to claim they were cheaper than Kroger. We shopped at HEB for a while but I noticed that we spent more money there so back to Kroger. Now we do Food Town and Kroger. Kroger is generally better on produce but FT has some things we like that Kroger doesn't. You just got to know your stores and prices.
There is a Brookshire Brothers up at the lake, and we keep an eye on their weekly flyer, but it's a bit of a trek, and with the population explosion around here, it's hit or miss as to whether you can get what's been advertised. We used to have an Albertson's, and we always comparison-shopped between the two, but they closed down a LONG time ago. No one else wants to move into our town, and I recently read an article somewhere saying that it's because no one thinks they can compete with HEB.
Whenever I get to ATX or SAT, I do like to go prowl around Trader Joe's and Whole Foods. More recently, I was able to make a stop at Wheatville Coop. That was a lot of fun. None of those are less expensive by any means, but they have some of the more uncommon goods.