When the public owns the infrastructure, there is enormous political pressure to price service too cheaply, which can work in the short term but has led to the infrastructure disaster we're seeing in the U.S. now: https://www.infrastructurereportcard.org.
Texas electricity was privatized, and they got inexpensive, dependable electricity. It also hasn't held back renewable energy construction, Texas has chosen to utilize its immense wind potential for example.
California by comparison has electricity rates nearly twice that of Texas. For 2015, the Texas number was 8.64 cents per kilowatt hour (ranked 10th least expensive), while California was at 15.5 cents (ranked 9th most expensive).
So now TX electrical companies are just a bunch of middle men. They only compete on price and customer service, and price IIUC is basically a margin game of futures and size, not actual electricity innovation. By law, only one company can setup the lines, fix the lines, etc. Not sure how privatized that is if it's the state by another name.
I'd say the privatization or lack of between TX and CA has little to do with costs or quality. In this case, CA just had a bad company and TX a better one (or ones).
CA electricity was privatized, and we got Enron.