matching field of view between apsc and full frame

Is the field of view the same for an aps-c body with an aps-c lens on it and a full-frame body with a full frame (FE) lens on it?

Not if both lenses are the same focal length. Focal length is a property of the lens, not of the sensor size. Angle-of-view (AoV) is a property of the focal length and the sensor size combined. AoV is what we use crop factors for when comparing what focal length we need to get the same angle-of-view using different sensor sizes.

Look at it this way. If you have a 50mm FF lens on an APS-C camera and a 50mm APS-C lens on an APS-C camera, the focal lengths of both lenses is exactly the same, the angle-of-view you'll see with both is exactly the same, and both 50mm focal lengths need to be multiplied by the crop factor to tell you what angle of view you will have compared to a FF camera. In the case of Sony APS-C cameras, any 50mm lens will give the same angle-of-view on a Sony APS-C camera as what you'll get with a 75mm FF lens on a FF camera.

It doesn't matter if the lens you are using on your APS-C camera is an APS-C only lens or if it is a FF lens, the same focal length will give you the same angle-of-view on the same APS-C camera.¹

For whatever angle-of-view you see on your APS-C camera with a particular focal length lens (APS-C or FF), if you want the same angle-of-view using a FF camera you need to multiply the focal length of the lens you're using on your APS-C camera by 1.5X.

18mm on APS-C is the same AoV as 27mm on FF, so get a 28mm lens.
24mm on APS-C is the same AoV as 36mm on FF, so get a 35mm lens.
35mm on APs-C is the same AoV as 52.5mm on FF, so get a 50mm or 55mm lens.
50mm on APS-C is the same AoV as 75mm on FF, so get a 70mm or 85mm lens.
70mm on APS-C is the same AoV as 105mm on FF, so get a 100mm or 105mm lens.
85mm on APS-C is the same AoV as 127.5mm on FF, so get a 135mm lens.
90mm on APS-C is the same AoV as 135mm on FF, so get a 135mm lens.
100mm on APS-C is the same AoV as 150mm on FF, so get a 150mm lens (if you can find one).
135mm on APS-C is the same AoV as 202.5mm on FF, so get a 200mm lens.
200mm on APS-C is the same AoV as 300mm on FF, so get a 300mm lens.

It's that simple.

_{¹ Within the limits of the actual versus marketed focal length of the lens, that is. Most lenses are rounded up or down to the nearest "standard" focal length. Both a 33mm lens and a 37mm lens will be marketed as 35mm lenses. Both a 189mm lens and a 203mm lens will be marketed as 200mm lenses, and so on.}