Saturation current on chip inductors
Looking at the datasheet of the "chip inductor", page 2: Inductance over current, I conclude that only up to about 100 mA this inductor behaves "properly".

The other inductor has a similar plot, also on page 2, from which I would say that it is usable up to 600 mA.

That's a 6x difference!

Only if you are 100% sure that your application keeps the current through the inductor always below 100mA would I consider the chip inductor.

Note that depending if we're dealing with a buck or boost converter and what the input/output voltage ratios are, the momentary current through the inductor can be many factors larger than the (average) currents going into and coming out of the converter. In extreme cases the current through the inductor can be 10x as high or even more.

The chip inductor is physically smaller and has a different construction so it simply is less capable at storing magnetic energy.