The clamp meter with line splitter approach, of course, will
NOT allow you to measure power factor, and that actually is quite important, particularly for something "below 1W in idle" like a switch mode iThing charger unloaded.
The Kill-A-Watt will do this "properly," though not with enough precision to be very useful for < 1W loads.
I actually own the Antai device. It does have a bit more resolution and sensitivity, and seems to be accurate, too. I have one. However, mine is not useful for long term energy measurements because it reliably locks up after a few minutes. Also, the manual is the impenetrable in English. Here is an old thread on my unit:
https://www.eevblog.com/forum/testgear/teardown-antai-atx-9801-handheld-plug-power-meter/msg613966/#msg613966. Note that someone else has one and his does not lock up.
I went through this whole saga awhile back, trying to measure the power draw of some unloaded small PSUs. In the end, if you need accuracy, you need a decent instrument. Look at the Chroma 66201/66202 for a decent baseline single-phase instrument. For more coin, look at the Yokogawa WT210/WT230. Hioki also has one PW3335. One useful keyword to search for is "IEC 62301" which is the standard for standby power for which many people who buy such meters are gunning.
I believe Dave also a nice unit, a bit cheaper, but in the same general class. Can't remember the name.
Oh, and there is the Gossen Metrahit Energy which Dave also likes. Plus: handheld and useful as a DMM.
One other thing: you can modify the shunt in a Kill-A-Watt to make it more sensitive. You basically will remove the shunt and replace it with a higher resistance. Since this is hard to do accurately, you will essentially get garbage current/power measurements, that you will need to scale appropriately. Of course, to determine how much to scale, you'll need some known load that was measured by some other means.
Finally, if you
really want to do this right, you probably want a programmable AC source, as well as a power meter. Some of these have integrated power meters, too. BK Precision 9801 looks nice.