In order to improve the Geico ad, I would advise them to tell more about their services and actual savings rather than concentrating so much on the gecko. For example: While the Progressive spokesperson "Flo" is highlighted in all of their advertising, she spends time talking about their goods and services rather than ring-tones and disco balls.
Geico obviously targets consumers more concerned with meeting their legal insurance obligations cheaply than any other consideration, yet they do not show to this consumer's satisfaction that they can actually do so.
As for the Allstate ads, since you posted this question, they have begun a new campaign with a disreputable-looking character who symbolizes mayhem. The first few ads were confusing and somewhat repugnant, but as the series continues, it grows on the viewer.
The main thing that Allstate has improved upon is that it has highlighted what it offers better than what the competition offers. Unlike Geiko, Allstate is obviously targeting the consumer who wants more comprehensive coverage versus minimal liability, and the new ads to an acceptable job at this.
However, the rule of thumb with advertising of any variety is that the consumer must remember both the ad and what product or service is being offered. Additionally, the consumer must rememberr the ad in a positive light for it to have a positive effect on the bottom line. For example, in the new State Farm ads, the spokesperson constantly interrupts the agents that he is supposedly interviewing and badmouths the competition. He doesn't so much make his case that State Farm has more to offer than the competition, only that more people were (possibly) dumb enough to use them than their competitors. The net effect of those ads is to turn me away from using State Farm, even though I have had positive personal experience with them.
With that in mind, I woiuld suggest that Allstate could have made the unattractive and disreputalbe Mayhem character secondary and put someone more likeable as the spokesperson.