Generally, when reconfiguring like this, its because you have a different line voltage.
The overall current rating of a machine like this is based on the allowable current through the windings (heat dissipation of the I^2R losses).
So going from star to delta, if you keep the phase current in the windings the same, the line current can go to sqrt(3) times larger. To keep the phase voltage applied to the windings the same, you need to reduce the line-line voltage by sqrt(3). So net effect is the same power rating.
You need to be more specific. Are you reconnecting the motor windings, in which case the line voltage is the same, or are you reconnecting the supply transformer, in which case the line voltage changes, or both?
Reconnecting from star to delta is putting sqrt(3) times higher voltage on the windings in each phase. This will increase the magnitizing current needed. If the iron saturates at this higher voltage/coil, the current will be excessive and burn up the motor.
If the iron *doesn't* saturate, and the magnitizing current is not too large, then the motor would be capable of sqrt(3) times the power (same current per phase in the windings, sqrt(3) times larger line current and at the same time same line voltage but sqrt(3) times higher phase voltage).
But chances are any motor of appreciable size (integral hp and up), if not specifically designed for the higher phase voltage, will burn up in short order.
So "the effect on the motor rating' is most likely, "1.73 times higher power, for about 10 minutes, followed by 0 power"
------------------- The difference is negligable if you stick to ratings. Given a set of windings, there is a rated current per winding as well as a rated voltage per winding. Based on these the KVA rating doesn't change and as the apparent R/X ratio, power factor at any given slip don't change, the KW wont change. What does happen is that the rated voltage/current in Y is not the same as the rated voltage/current in delta even though the product VI is the same.
If you take a given set of windings in Y and reconnect them in delta at the same line-line voltage, the current will be higher by root(3) and the torque will also be higher by a factor of 3 but this is temporary-lasting only a short time after you smell the magic smoke leaking out.