At least have them as closely match as possible. You can always change the feel of a room through wall color and accessories.

Keep them matching as closely as possible. I've seen homes with several different kinds of wood flooring and it never looks good.

Certainly wouldn't want to confuse matters, but you don't indicate what your "existing" oak floors are... oak floor is all but a generic term in the floor biz.

For example, if the old flooring is a 3/4" x 2-1/4" Red or White Oak... & if you were able to determine which and supply a color sample, there are those of us who can "simulate" the same floor in a prefinished fashion, that may not be a PEFECT match, because of the time differential... (one is old, and the other is obviously new), however you could definitely get close enough to have them look natural together... rather than going for a "night & day" difference...
Which the other guys are suggesting... keep them related/similar.

Right now I have the original old 3/4 x 2 1/4 red oak in the kitchen and dining area. We replace the dreaded blue carpet from the eighties in the hall and living room with engineered hardwood that blends nicely with the old oak although it is cut wider. When I had the whole interior repainted I chose different colors for the rooms that are off the main living area. They are all painted in pale muted that I consider neutral. I decided not to go with the " All room should be the same color throughout the home so it flows." school of thought. It seems to flow quite well as all the colors are soothing. I thought since I was such a rebel with the paint colors I might push the envelope further with the flooring. I tend to agree with everyone who thinks the floors should be the same or related. I just wanted to hear what others had to say.

Thanks to all who have given their opinion, it is much appreciated.

I have seen many older mansions in my travels with mixed flooring. Also it is proper to turn flooring to match width of room meaning parallel to the longest walls, this in and of it's self can provide perhaps the look you are searching for. Another is staining after sanding the floors can bring a fresh look.
Jnadiane a rebel knows, Continuity is just a measure of resistance :)
Steve