What is the main difference between 13 watt and 23 watt flourescent lightbulbs?

I'm trying to save on electricity and contemplating replacing all the incandescent bulbs to fluorescent. Which should I pick, the 13 watt ones or the 23 watt ones?

Help me out with the math, please. So if I pick the 13 watt bulb, used it 24 hrs a day for a whole month, I'd be using 9,360 watts or 9.36 kilowatt hours? At my rate of 0.075 per kwh, that's $0.702. If I didn't replace the 75 w bulb, my bill would be $4.05. If my math here is correct, that'll save 83%. Am I doing this right?

Your math is correct. To save money and energy go with the 13 watt. You may want to use a mix depending on location. The 13 watt bulbs may not give enough light for all applications. I have some CFLs that take about a minute to get to full brightness. The start out a bit dim and pink. As they wam up they change to a more normal color and brighness.

If you are wanting to conserve go with the 13 Watt. they use less energy, BUT check the actual lumens output of the bulb. compared to the equal incandescent this is where the issues are.

Ten watts .

The 13 watt is equivalent to about 40watts incandescent and the 23 about 75 watts It depends what type of fitting its going in as well because the 23 watt is considerably bigger.
If its going in a central pendant light fitting go for the 23 watt.

the 23 watt one is brighter and 10 watts costlier.

10 Watts..............
If you are contemplating switching to fluorescent bulbs, the comparable wattage rating for each bulb should be listed on the packaging. It's a matter of personal taste. However, picking the lower wattage alternative will generally be dis-satisfying for your needs. Buy the higher wattage bulb and test the brightness for your application. Since you cannot return the bulbs, because you're not satisfied, use common sense and have an alternate plan to use them in other areas.

Light output, and load.
The 23W. CFL puts out about 1100 Lumens,
(about as much as a 100W. incandescent bulb).
The 13W. CFL puts out about 600 Lumens,
(about as much as a 60W. incandescent bulb).