I love to cook and entertain, so I spend a lot of time in my kitchen. For the purpose of not suffering leg or back pain from standing on a rock hard tile floor, I prefer a softer place to stand. Also, anything that drops on a tile floor will shatter in a gazillion pieces, no doubt about it.
Wood floors are fantastic, IF they have the correct finish AND are swept every day. Otherwise, dirt particles on the floor (from shoes worn outdoors) will act like abrasive pieces of sand paper and wear out the finish and scratch the floor in traffic areas. Also, I have wooden kitchen cabinets and oak butcher block counter tops. So, putting down a wood floor with the wood cabinets and oak counter tops is waaaay too much wood in one room for my taste.
Therefore, for those reasons, I prefer sheet vinyl as it is totally waterproof and lasts a good long time. You also cannot beat the easy maintenance and the fantastic price either.
BUT, if I had to choose between tile or wood, I would pick wood. With all of the fantastic finishes available today, and with good upkeep habits, wood floors are truly beautiful. All of my bedrooms and common areas in my house all have wood floors and I love them.