I prefer the two 9V myself as split supplies.
Yes you can run one battery and use a resistor voltage divider with a filter cap, and it works just fine, but if you can use two batteries, that's less parts you have to use and you get a better voltage swing with 2.
I use the +/-9V battery supply when testing freshly built amp circuit, so I can get the amp working on lower voltage, before I give it the "real" power from the mains transformer. If you accidently short the 9V batteries, no smoke most of the time.