Stefan,
   It may be that all (or an unintended mixed subset(i.e. 1 log, 2 DB and
3 STGPOOL disks) of the disks are on a single I/O channel resulting in a
bottleneck on the data path.  This would be reflected by high IO (combined
DB,LOG and STGPOOL activity) during a backup to disk while comparatively
little data is actually being transferred.
When you backup directly to tape, only the DB & LOG disks are used - not
much contention.  When you write using simple file copy, only the STGPOOL
disks are used - again not much contention.  When you backup to disk, all
disks are used and there may be contention on the I/O channel due to the
mixed workload.
You may be able to identify this using perfmon and monitor individual disk
queue length & read/write time and activity or simply review the physical
disk connections to ensure they are not on the same path.

Cheers,
Neil Strand