You can open a MainStage patch in Logic since MainStage and Logic both share the same software instruments and plugins.
You can save the channel strips you'd like to use, and then add those to your project inside Logic. You will want to save them in the folder Audio Music Apps > Channel Strip Settings > Instrument and then you can pull them into either MainStage or Logic. You will be able to view them under "User Channel Strips" in Logic. You'll want to click on Input > Save Channel Strip Setting to do this.
If the channel strip you'd like to save is an audio channel strip, you'll need to save it inside the folder Channel Strip Settings > Track Then, inside Logic, you'll go to User Channel Strip Settings > Track and then it will show those channel strips exported out of MainStage.