The Apache license is "sublicenseable":
- Grant of Copyright License. Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable copyright license to reproduce, prepare Derivative Works of, publicly display, publicly perform, sublicense, and distribute the Work and such Derivative Works in Source or Object form.
I can therefore create a derivative work of Apache-licensed code under any license I please BUT I still must abide by the terms of the Apache license itself, including keeping notices, license texts, change tracking, etc and both license terms will apply.
Therefore, sublicensing using a BSD is a rather moot point and I would rather instead keep thing under the Apache 2.0 license.