Sleeping
Rim-weighted yo-yos will sleep longer, plain and simple. The design of the sb2 is a good example... the sides are hollow and all the weight is on the rims. To increase sleep time in a yo-yo, add weight to the rims. Several yo-yos, most notably Team Losi and the SB2, come with weight rings that can be added to the rims (pictured). Otherwise you can make them.

Looping
Center-weighted yo-yos flip easier, and are thus preferable for looping tricks. Center weight does not increase sleep time significantly. A good example of a center-weighted yo-yo is the Russell. It has a large plastic hub on the center of each side, then small rims. Team Losi yo-yos come with center weights (pictured).