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I have two feature classes containing building footprint polygons. Both are of the same area and can be superimposed (not 100% but very close). However, they do not have the same attributes. Therefore I would like to merge the attribute tables so I have the full set of attributes in one feature class.

But there's no common identification field between the two classes, so how can I link each polygon in the first class to its matching polygon in the second and merge their attributes?

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There are more than one way. I would try Spatial Join with match option

HAVE_THEIR_CENTER_IN —The features in the join features will be matched if a target feature's center falls within them. The center of the feature is calculated as follows: for polygon and multipoint the geometry's centroid is used, and for line input the geometry's midpoint is used

To join the attributes from one building dataset to the other.

You will have to choose which of the two datasets geometries you want to keep.

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