I would never introduce 2 dogs on either one's turf. Find a neutral point, park, ball field, walking down a sidewalk that neither one normally walks, so there is no territorial feeling from either one. Keep both dogs on leash, not tensing up but calmly let them do the whole sniff and check out greeting. If all goes well, walk them together and let them continue to get to know each other. I would probably introduce them off property, more than once, prior to taking them in either dog's house, if you are concerned about either dog. When you do take them into the house, I would keep them on leash and not leave them alone at all, unless you see something, eating side by side, laying side by side, playing nicely with each other, etc. that convinces you they will be okay together. This may sound like overkill, but I have seen and heard about disastrous consequences from introductions gone horribly wrong. My son had to take my springers to his house once. My dogs had never been to his house and he had 2, 2 year old male pit mixes. My dogs walked in and the female grabbed one of his males and would not let go. He finally got them apart and after trying to resolve it, ended up having to keep his dogs in his bedroom for 2 days, until he could bring my dogs home. My female would lay outside his bedroom door growling. When he took his dogs out, she would watch them out the window growling. This is the same dog I could take anywhere, dog parks, etc. and she never had a problem with any dog, anywhere. Taking a dominant dog to another dog's house does not automatically resolve the issue. Better safe than sorry. Good luck.
Kathy