Mobile phones will always be the best option for hearing aid users for two reasons. One is the direct Bluetooth connection that most modern hearing aids now have, cutting out background noise and feeding the caller's voice through both hearing aids simultaneously. Two is the full frequency bandwidth of a mobile versus the reduced bandwidth of standard landline connections.
However, if you or your relative cannot use a mobile, you should look out for "Hearing Aid Compatible" (HAC) landlines.
This refers to the tendency of phones to cause interference in hearing aids. An HAC phone is less likely to cause interference.
Within the banner of Hearing Aid Compatibility you have the M (microphone) and T (telecoil) rating. They go from 1 to 4, with 4 being the best (least interference).
To use the T facility of the phone, your hearing aids must have the Telecoil component on board, and you must switch it on during the call. A phone can have telecoil function but still be a poor quality signal (T1) whereas a telecoil compatible phone with T4 rating is going to have better quality sound in comparison.
You should also consider a speakerphone option where possible, to avoid any interference. I feel that any method where you're hearing using both aids is an advantage over one.
In terms of sound quality then, top to bottom:
Mobile phone with direct Bluetooth connection (e.g. Made for iPhone aids)
Mobile phone on speakerphone setting
Landline that's HAC with M4/T4 rating, using the telecoil function of your aids
Landline on speakerphone in a quiet environment.
These ratings/compatibility are a guide and some phones just aren't as good as others in terms of their sound quality. If the phone is an important part of your life, I recommend asking questions about phones when purchasing aids, and asking questions about aids when purchasing phones, to ensure you get the best setup for you. Choose a supplier with a money back guarantee so you can test it out, and don't be afraid to learn new methods or try new devices.
Above all, if you have a choice, choose an audiologist who understands how important the phone is in your life. They will help you to choose and use the right equipment to keep you in touch with your loved ones or help you navigate your work needs with confidence.