Both Premiere and Encore use the same encoder, but the default settings may be way different. Try this in Premiere;
1. In the Export Settings window, click the video tab and change the Quality slider to 5.
2. Change the Bitrate Encoding to CBR and the Bitrate to 8 mbps. This will force 8 mbps.
3. Most important, deselect Deinterlace in the Output Module (upper left corner). This will prevent reducing the resolution by half.