As with most equipment, we have become accustomed to determining our needs relative to power handling capability and the output power being used. However, when it comes to baluns and ununs, this rating or capability should not be used as a primary decision maker. The reasons for this are many and varied but here are a few of the most important.
When a balun or unun is wound correctly, which is an important differentiator, a higher power rating will also mean a higher efficiency, low SWR and excellent overall Return Loss. Consequently, if you're a QRP operator running 5 or 10 watts, the best choice for you may well be the balun rated at 3 or 5kW. Of course this is usually impractical if your intended use is portable operation and want something small and light, but for a permanent installation the higher power is a much better choice. Keep in mind this may not be the case when using an inexpensive balun rated at high power. It is almost impossible to build a $20-30 balun that also offers high efficiency.
RFI in your shack, house, neighbors etc is another consideration. Many times to maximize choking impedance we will use two toroids in a stacked configuration. This also increases power handling but the primary design focus is the amount of common mode current that can be eliminated by using the two cores. Power handling is just a secondary resultant, but is always beneficial.
In addition to efficiency, another consideration should be the antenna being used and the conditions a balun or unun may be subjected to in the antenna/feedline circuit. Baluns and to a lesser extent ununs, lose power handling rapidly as VSWR increases. In fact and again when built correctly, at 2:1 they will lose 30% of their rated capacity and more if one of the “cost effective” brands is used. This means that when running 500 watts, a balun rated at 1kW will be close to maximum power handling if the VSWR at the feedpoint is 2:1. At 3:1 SWR the same 1kW balun will be subject to a failure commonly referred to as saturation and in some cases extreme overheating. This is why you see poorly built 3kW baluns fail at power levels of only 500 or 600 watts. Just because your tuner can create a match does not mean the balun at the feedpoint is not being overstressed.
Utilizing well designed baluns/ununs built with quality components will provide the highest level of performance and power handling with the lowest chance of failure.