Tile b/c you'll never be able to match the wood.

What is in the room with the (current) white tile? I agree that matching wood is difficult.

I think the answer depends on what the rest of your home's style is...

Slate can be nice. Tile can be too. Marble. Carpet.

We need to know a bit more.

Bottom line: I think we're all recommending not trying to match the wood.

I would install wood flooring and match as close as possible in grain pattern, board length, and stain color. If you sand and refinish the existing floors, everything would match but a good flooring guy can get very close to existing look on your new flooring.

If you are concerned, you can run the new flooring on a diagonal to hide a slight color difference or inset a transition strip or border of a different wood to keep the two surfaces from direct contact.

Thank you all for our advice! It's very helpful.
The kitchen, dining, living room, entry foyer and master bedroom all have the oak.
The tile hallway leads to a large family room that then leads to another hallway where additional bedrooms are. It's like another wing if the house connected by a hallway transition.

Here are some pics of house ... The arched entrance on the right is where the hallway is with tile... This is not my decor , we still have not moved.

I'm sure you are excited to move in to that house...it looks like a nice home .If you haven't moved in yet, I would suggest living in the home for a while before making any expensive and permanent decisions.

Even if it doesn't match perfectly, I don't think you can get the look and feel of wood flooring with anything but the real thing.

If you have solid oak then a professional installer should be able to feather in new unstained oak with the old, sand the old oak, and then stain it all whatever color you want. We just did exactly that a few months ago and it's gorgeous. It all matches exactly because of the technique, even though the original oak floor in the one area was about 20 years old. It was pricier than buying prefinished, but you can't beat solid hardwoods. Call a hardwoods installer and have them take a look at what you have and give you so e options. Good luck!