Woven fabrics - Knitted fabrics
Knitted fabrics vary - some stretch only one way - some stretch both ways - some stretch in every direction - some stretch a l-o-o-o-t - and some do not stretch at all.
My suggestion is to sew test samples of any knitted fabric before attempting to assemble the "real" pieces. Sew some crosswise, some lengthwise, and some with one piece "crosswise" and the other "lengthwise"
Once upon a time, I basically thought that a knit was a knit was a knit. Oh, how wrong that idea was.
Even some wovens seem to have more stretch/give in one direction than another. Making test samples with wovens "will not hurt".