According to Creative Biolabs, the primary differences are:
In the screening/panning step, yeast display is suitable for Fluorescence Activated Cell Sorting (FACS), allowing to sort out antibodies with desired binding properties precisely. However, the affinity of antibodies to antigens in phage display can only be roughly stratified (sorted into categories of goodness) by adjusting the washing buffer compositions.
Owing to its eukaryotic expression system, yeast displayed antibodies can be correctly folded and modified, such as [...] to be closer to their native structure in mammals compared to the antibodies expressed by E.coli in phage display.
The diversity of yeast displayed antibodies may be lower than phage (107-109 for yeast, up to 1011 for phage), due to the low transformation efficiency of yeast.
Due to the many more copies of antibody on yeast surface (104-105) than phage, it is possible to select out low affinity antibodies according to antibody avidity with yeast display system.
Anecdotally, phage display is also cheaper.