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The photo with barlow has more definition than the photo by projection of eyepiece. You see more details.
Barlow change the focal length. eyepiece cause amplification.
With change of focal length of telescope you have an increase of resolution. Aparent amplification.
For astrophotography with projection toward sensor of a camera the image from barlow (with good quality or small spheric distortion) will have always better definition than eyepieces projection.
note: barlow is a negative lens; don't amplify. Mirror (spheric or parabolic as used in telescopes) don't amplify, it reduces the image. Sensor of camera isn't lens, therefore it doesn't amplify. The aparent amplfiication of barlows is actually increment in resolution.
Use of barlow has limitation by refraction. Barlow 5x needs good seeing to produce good results. Because this a 2x , 2.5x or 3x is more useful.
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