These are video cameras, but the basic principle is the same as with still cameras: the FDR-AX100 has a much larger sensor. It is a 1" type, while the FDR-AX33 has 1/2.3" type sensor. (These formats are common in still cameras too, with the 1/2.3" size being prevalent in compact point and shoots and 1" becoming more common in higher-end compacts and a few interchangeable-lens systems).
The 1/2.3" sensor measures about 6.17mm × 4.55mm, for a sensor area of about 28.50mm². A 1" sensor is about 13.20mm × 8.80mm, or 116mm², four times the area. In photography, we normally think of metering, exposure, and light-gathering ability in terms of "stops", where each stop is a doubling or halving — so, 4× is two doublings, or, a two-stop advantage.
Meanwhile, going from f/1.8 to f/2.8 is about one and a third stops. So, even with the faster lens, the larger sensor has an advantage.
Of course, that's assuming the underlying technology is basically the same. Sensors can also vary in fundamental sensitivity and noise levels as well, so this is only a general guideline.
Oh, and also: if you view at the same size (which presumably you would, with video), the difference in sensor size also affects apparent depth of field, with the effect approximately equal to the ratio of the sensor's width or height — so in this case, in terms of depth of field, f/1.8 on the smaller-sensored camera will give approximately the same depth of field as f/3.6 on the larger-sensored one, assuming the same framing. (Or to put that another way, if you want more shallow depth of field, you can get more from the FDR-AX100, even though the lens is slower. With either camera, assuming the light is good, you can stop down for more depth of field — more of the scene in focus.)
If the FDR-AX33 had an f/1.4 lens, both of these factors would just about exactly cancel each other out. (Since f/1.4 to f/2.8 is two whole stops.)