Like the X-Pro1 the X-E1 shows visibly higher resolution in this chart test than a conventional 16MP Bayer-type camera such as the Nikon D7000, or even the Sony NEX-6 (which has a particularly weak AA filter). In fact, in terms of resolution the Fujifilm is very close indeed to the 24MP Sony NEX-7 or the Sigma SD1, which uses a 15MP Foveon X3 sensor to record full color information at every pixel, and therefore (like the X-E1) uses no AA filter.
These chart shots also show very little of the false color that we'd expect from a Bayer camera with no AA filter - there's a little on the RAW version, just around the point where the X-E1 begins to struggle to accurately resolve the lines on our chart, but none at all in the JPEG. This supports Fujifilm's claim that the X-Trans CMOS is less susceptible to moiré than a Bayer sensor. Last but not least, the X-E1's JPEG processing can deliver just as much resolution as the converted RAW. We were impressed by the X-Pro's and X100's JPEG processing, and the X-E1 lives up to the same standards.
As we often see for a camera with no AA filter, the X-E1 continues to show line structure beyond its Nyquist limit. As usual this is false detail (i.e. it's not an accurate representation of the chart) but in real-world use it often helps give an impression of increased detail anyway.
DPReview.com FujiFilm X-E1