I have a small active antenna next to a 102ft flat top dipole (G5RV) at about 35ft height and have compared them extensively.
The active antenna is a semi kit described here:
http://www.arrl.org/files/file/Technology/tis/info/pdf/0109031.pdf
Much of my HF use is 40 and 80m NVIS within a few hundred miles where a low horizontal antenna is desirable and the G5RV outperforms the active antenna in signal to noise ratio and the active antenna has a higher noise floor. Signal levels vary but are not that much different between antennas much of the time. I would say the G5RV would pick out an extremely weak signal better than the active antenna in this mode.
On higher bands where distant signals are arriving at a lower angle and the vertical polarized active antenna is more appropriate it does a very good job and the differences between the antennas are less but the G5RV is still quieter and can generally pick out a very weak signal better than the active antenna.
On the AM broadcast band and below is where my particular active antenna really shines bringing in signals way stronger and in some cases better signal to noise than the G5RV. If a signal is copyable on these low frequencies on the G5RV its usually a bit more pleasant to listen due to the lack of noise but at some point the active antenna brings them way out of the noise even though the noise floor is also brought up but the signal to noise ratio can still be much better on the active antenna on VLF.
I don't use the active antenna much since the G5RV and other HF antennas here do 99%of what I need but if the AMRAD active antenna was the only HF receive antenna I could have due to space it would not be too bad.
The AMRAD is a semi kit that cost about $75 to build and it performs in the range of $300 to $500 assembled active antennas. An inexpensive active antenna would not give results anywhere close to what the AMRAD does due to overload and generation of Intermod and the results here would be greatly skewed toward the G5RV in that case.
So in a nutshell a really good active antenna will probably make most SW and HF users fairly happy in my opinion.
prcguy