If you use the phones a lot, an IP phone system will allow you to make or receive a call on any phone, while another is in use (though you can also accomplish that with the proper analog phone setup and multiple ATAs).
You have more flexibility in handling multiple calls. For example, you're on a call and put it on hold to answer another. You can transfer the new call to your wife (at home or on her cell) and then resume the original conversation.
Some ATA configurations have problems with DTMF transmission, DTMF talkoff, or echo heard by the remote party. These issues are very unlikely with an IP phone. Doubletalk performance is better with IP phones, though not perfect.
Recent IP phones support wideband codecs, often called "HD voice". This offers vastly improved voice quality, but is unfortunately presently available only when your contact is using the same provider, e.g. both on Callcentric or both on
VoIP.ms, or if iNum or other peering is available between them. Of course, your contact must also have an HD phone.