The feature differences you described between the phone and the ATA are firmware-based, not hardware.
If you make a pure SIP VoIP (not traversing the PTSN) call with the 1032, and if the phone on the other end supports Opus, then the call may be using Opus, not G.711u. There are some very good articles on the web that explain how Opus works, so I'm not going to type it out here. If the call is using Opus, then the OBi 10x2 IP phone will display a "HD" logo on the LCD. For example, you can have an Opus HD Voice call between two IP phones via Callcentric 1777xxxxxxx extensions, because it's a pure SIP VoIP call, not traversing the PSTN. You can do the same thing via the OBiTALK network (from one IP phone, call **9xxxxxxxxx, where the x's are the OBi number of the other phone).
If you want to compare audio quality between your IP phone and your ATA, I suggest that you try calling one OBi number from the other.
The overall audio quality of the IP phone is going to be better, because it has one less digital-to-analog conversion, and it is not constrained by the limited frequency range specified for PSTN calls. The handset is a piece of plastic with a microphone and a speaker in it. It is only one part of the entire system. Since there are millions of analog telephones out in the wild, there is no way to know the design and manufacturing quality of the microphone and speaker in a random telephone. However, the handset in the OBi IP phones are specifically designed for wideband audio along with the rest of the audio electronics in the phone, such as the amplifier, whereas the handset in the analog telephone is designed for narrowband audio.
The overall, end-to-end audio quality has many variables, including hardware, network, firmware and the human's hearing. Audio tests, be they with a telephone, or with amplifiers, speakers, etc, are always highly subjective, and things like the volume level need to be precisely set to be equal for both devices under test. For example, subjects may perceive louder music to sound "better" than lower volume music.
So, bottom line, without expensive test equipment, you can't make a truly valid comparison test as you described. In my own extensive testing of OBiTALK products, if using a good quality analog telephone, sound quality on that phone plugged into a OBi 200/202 is very close to the sound quality of the IP phones, on a narrow-band G.711u call. Sound quality on a properly functioning IP phone<-->IP phone call on a ITSP that supports Opus is fantastic.
Finally, one set of variables you can experiment with are the transmit and receive levels on the ATA, and the volume and gain settings on the IP phone. On the phone, they are in Expert mode, under user settings-->user preferences. If the settings are too high or two low, they can adversely impact the sound quality.