Is anti-reflective glass as clear as normal glass?

Almost. If the photo or artwork sits directly against the glass, the view through is clear and crisp and the difference with normal glass is hardly noticeable. If there is space between the glass and the image, the image looks slightly less sharp.

Why is it not fully transparent?

The anti-reflective side is matte and scatters the light. This removes most reflections, but it also means anti-reflective glass is not as fully transparent as normal clear glass. The greater the distance to the image, the more you notice this.

In a picture frame

In a picture frame the image almost always sits directly against the glass. The view through is then clear, and the only difference with normal glass is that distracting reflections are largely gone. In product photos the glass can look less transparent, because the object there often does not sit directly against the glass. In a real frame the image actually shows to its best advantage.

What anti-reflective glass is exactly, you can read in What is anti-reflective glass and when do you use it?.