Pick any two: size, bandwidth, efficiency.

I see a lot of people comparing the mag-loops to full size dipoles as if they were equal options. Electrical small mag-loops are a compromise antenna. Just by normal physical considerations it is obvious that a mag-loop is a much less sensitive antenna than a full sized half wave resonant dipole. Before even talking about the trade-offs in size vs impedance bandwidth vs efficiency and chu-wheeler-etc, there's effective aperture to consider. At HF frequencies (1-30MHz) the near field of some tiny LC oscillator (like a 1m mag-loop) is pretty damn large. But it is not as large as the size of a 1/2 wave dipole. So from the start a full size antenna is just intercepting *more* energy. Efficiency or radiating (and so reception because they're reciprocal) scales proportional to the physical path in space the currents travel over relative to wavelength. If the effective aperture doesn't subtend a decent fraction of a wavelength you just don't get, or emit, effectively. Electrically small mag-loops will always start ~20 dB down from the performance of a loop, or a dipole, that is a good fraction of a wavelength in effective aperture. And even just to get that relatively okay performance the impedance bandwidth is proportionally tiny.

You can, of course, get back a lot with LNA for reception. That's the beauty of radio, the absolutely boggling scale of power magnitudes over which it can work and still pull out the information. It's why you can stick your cell phone in a microwave but still get calls. A 30dB attentuation is a normal situation for a radio link and information can still be recovered. But the power... you lose most of the power in the first 6 dB loss. And that's why wireless power transfer will never work and microwave oven doors and electrically small mag-loops do.