Æthersnatch with Options

[mickeven]

If I {Æthersnatch} my opponents {Crux of Fate}, do I get to choose Dragons or non-Dragons?

[particle]

No. Modes are chosen as part of the casting of the spell. Changing the controller won't change the modes.

[griffin131]

No. Choosing new targets is completely different from choosing modes.

Mode has to be chosen before the spell is cast and you get priority.