Nationwide definitely has the catchier jingle! All joking aside, it's worth saying that Nationwide has lower premiums than Safeco on average. This is especially true if you have a bad credit score. Safeco's premium jump for scores lower than 580 is downright jaw dropping by comparison. Nationwide is also a little more forgiving to drivers who have points on their license.
If neither credit nor driving record is a problem for you, Safeco will have better rates.
They're about equal in customer service rankings, and Safeco's lists of optional coverages may mean that they work better for your unique situation. Both Safeco and Nationwide have a program that helps you get rid of your deductible if you go long enough without claims.
Nationwide also has a mobile app and strong online services. If that's important to you, then Safeco might not be the best choice.
Safeco vs Nationwide: If you prefer person-to-person service instead, then it may come down to making an apples-to-apples comparison of rates vs. service.