We simulate the tidal disruption of a collisionless N-body globular star cluster in a total of 300 different orbits selected to have galactocentric radii between 10 and 30 kpc in four dark matter halos: (a) a spherical halo with no subhalos, (b) a spherical halo with subhalos, (c) a realistic halo with no subhalos, and (d) a realistic halo with subhalos. This allows us to isolate and study how the halos (lack of) dynamical symmetry and substructures affect the dispersal of tidal debris. The realistic halos are constructed from the snapshot of the Via Lactea II simulation at redshift zero. We find that the overall halos lack of dynamical symmetry disperses tidal debris to make the streams fluffier, consistent with previous studies of tidal debris of dwarf galaxies in larger orbits than ours in this study. On the other hand, subhalos in realistic potentials can locally enhance the densities along streams, making streams denser than their counterparts in smooth potentials. We show that many long and thin streams can survive in a realistic and lumpy halo for a Hubble time. This suggests that upcoming stellar surveys will likely uncover more thin streams which may contain density gaps that have been shown to be promising probes for dark matter substructures.