The first test is with each own's connection. See if both of you have a stable connection for general purposes (using social media, watching videos, downloading large files, like games...).
If you are safe about those, open Warframe, set your game mode to public and go to a popular node (alerts, boss nodes, infestation nodes, invasion nodes...) and see if each of you can connect to other people and have a stable connection with them. If you played the entire match with no Host Migration resulting in any of you getting back into the Landing Craft or in a Solo mission, you should have no big connection problems.
In my case, I have a pretty good connection in terms of bandwidth, downloading in a decent speed and using any website with ease, but I could only play Warframe games as a host, because if I entered as a client I would surely disconnect in the middle of the game.
Since Warframe uses the host's connection as a support to the game lobby, either you enter your friends game (and it works, because the settings may be different) or either of you should have your router checked for correct port forwarding and connectivity.
Hope I helped you troubleshoot, happy gaming!