I guess one question… have you looked at digikey for a 0603 10uF 50V capacitor?.. not at all common 
I suggest its a typo or someone just picked a size without going through the check list.
The question of capacitor size comes up a lot and little thought usually goes into it other than the board space available.
The size should concern engineers far more than just in passing.
In the case of 0805 vrs 1206, the 0805 capacitor is only 1.6 uF at 20V compared to 1.99 uF for the 1206. At 40V they are both down to 0.7 uF. This is due to ceramic capacitator’s ΔV/ΔC which is quite extreme with small capacitors. If, for example, you were to choose a 1210 capacitor instead, the same voltages will yield 5.8 uF and 2.6 uF. This is still along way from the 10 uF as specified.
Often, when the manufacturer specifies 10 uF, they will have already considered the ΔV/ΔC in their calculations.
One usual consideration, for longevity, double the working voltage for ceramic caps. So if you are on 9 V supply, minimum working voltage is 18 V. For consumer items, not so much of a consideration (1.5 times?).
In regards to your application… 9V, That’s only the input capacitor, the output capacitor is only 3-4V
At 4 V (SYS voltage) 16 / 25 / 50 V doesn’t matter so much nor does the package (0805/1206):
16 25 50
0805 4.9 6 8
1206 7.1 6.6 8.8
very little in it between 0805 and 1206, also between 16 / 25 / 50 V
as far as ESR goes, 1.3 MHz is the sweet spot for 10 uF so all are similar.
NOTE: This is from Samsung electro-mechanics web site and ONLY applies to their capacitors.
Different capacitors can behave very differently.
If you look at page 43 - 44 of the data sheet, then you will find the calculations for the input and output capacitors. These should be followed and the d voltage/d capacitance accounted for when choosing the capacitor size / values.
It is most likely that fewer capacitors will be required if you choose 50 V capacitors rather than 25 V capacitors.
The BATT output is technically a non switched output, Q4 is operated linearly so it is in effect a linear regulator so no switching, It is to keep the feedback stable, again <= 4V so no worries there. It also provides current peaks to your system load, this will help prevent dropouts due to the ESR of the battery.
One thing to note: The eval boards are often done by new-bees and interns, its the first projects a lot of engineers start with, and they are given recommendations. They also want to make sure you can easily swap components if you want to change the load or voltage for you “working board”. I’ve swapped 0402 resistors more than once… microscope required. at least 1206 you can see and pickup.
Simon