When we plot the co-polar and cross-polar radiation patterns in E-plane and H-plane and we put comparative analysis, then what can be the allowable difference between them can be considered for a good antenna radiation performance?
20 dB is good, but some systems require better than this - it depends on the use. For measuring RCS you might want 30 dB.
The cross-polarization tells you, for instance, how much of one communication signal breaks through into another signal, or how much loss is caused by multipath (circular polarization gives some immunity to multipath).
How much cross-polar performance is needed or is useful depends on what other factors are causing interference and/or crosstalk.
Cross-polar performance is not usually good over a wide range of angles.
Well, it depends on application. To be very specific you need min 30 dB cross-polarisation discrimination on axis (Theta=0, Phi=0) for a satellite communications. Hope this helps.