Increasing the voltage by that much will significantly increase the LED current - much more than you might think.
Most of those strips have 3- LEDs in series per section. The forward voltage on a Green or Blue LED is about 3.2V. The Red LEDs are about 1.7V each.
The intended voltage for those strips is about 12V. Let's use that as a starting point.
The increase in current for the Green and Blue LEDs is going to be about:
@ 12V: 12V - (3 * 3.2V) = 2.4V across the current limit resistors
@ 14V: 14V - (3 * 3.2V) = 4.4V across the current limit resistors
@ 16V: 16V - (3 * 3.2V) = 6.4V across the current limit resistors
So: increasing the supply voltage from 12V to 14V is going to increase the LED current by (4.4 / 2.4 * 100%) = 183%
Increasing the supply voltage from 12V to 16V is going to increase the LED current by (6.4 / 2.4 * 100%) = 267%
The situation is a little better with the Red LEDs. Doing the same math as above results in the following voltages across the current limit resistors for the Red LEDs:
12V: 6.9V across the current limit resistor
14V: 8.9V across the resistor
16V: 10.9V across the resistor.
That results in a 129% increase in current if running at 14V; a 158% increase in current if running at 16V.
I strongly suspect that the current limit resistors are going to be really unhappy. You will most likely also notice that the Red LED didn't get as bright as the Green & Blue LEDs at the higher voltages.
Bottom line: run the strips at the manufacturer's maximum voltage and feed power from both ends if possible.
An SMPS controller1 IC may support multiple converter topologies. But a single IC almost never supports all common converter types.
There is a family of converters derived from boost converter: flyback, SEPIC, boost proper. A controller that can do boost, usually can do the rest of the boost family too. Usually, one controller can't do both buck family and boost family.
1 SMPS controller IC drives external power switches. SMPS converter IC has power switches on board. Converter ICs tend to be less versatile than controllers.
Best Answer
The choice between using a simple 3 terminal linear supply and a switch mode power supply depends on the current you need, as well as the difference between the input voltages you have and the output voltages you need.
You did not specify the current draw requirements for the LED strip and the Arduino. You specify that you expect to use a buck converter for the LED strip, why is this? If the input voltage is only slightly higher than the regulated voltage, a high current low-dropout linear regulator will be almost as efficient, for much less complexity. Recall that the formula for efficiency in a linear regulator is Efficiency ~= Vout/Vin; if Vout is very close to Vin, then the efficiency will be close to 100%. A low-dropout linear regulator such as the LT1185 regulating from 15V to 12V will be approximately 80% efficient, which is better than many switch-mode regulators.
Your real question is how to power the Arduino, which runs at 5V. In this case, it is true that the efficiency of regulating from 12V down to 5V via a linear regulator will be poor, approximately 40%. However, your total power loss is proportional to current: P_loss = I_load*(Vin-Vload). The Arduino's exact current draw depends on which peripherals are enabled and what the code is doing, but assuming you are not doing much more than using the serial port to display some patterns, a current draw of 50mA is reasonable. Therefore, your loss in using a common linear regulator (such as a 7805) is only 350mW, which is reasonable if your application is not battery powered.