If you take an Energizer C or D cell apart, you will find that there actually is a Sub C cell in there.
Also, there are no Lithium Ion 9 volt batteries. They are Lithium Polymer. If your application is voltage sensitive, this is not the way to go. A Lithium Polymer 9 volt battery and two Lithium Polymer cells in it. These cells start out at 4.2 volts, but spend most of their life at 3.7 volts. This means that your battery starts out at 8.4 volts and spends most of its time at 7.4 volts. In contrast a 7 cell NiMh 9 volt battery starts out at a little over 10 volts and spends most of its life at 8.4 volts.
On top of that, you need a special charger for the Lithium Polymer 9 volt battery.
If your device has a voltage regulator, the Lithium Polymer 9 volt battery does offer a little more capacity, but if your device is voltage sensitive, this is not the way to go.