I sensed a disturbance in the Force and have been summoned...
"Tension" is a physical quality that is relatively straightforward to calculate for bass strings. It's a function of scale length, frequency (i.e.,, what note the string is tuned to), and what is called "unit weight," which is essentially how much mass an inch of string has. Gauge is the primary determiner of unit weight, but construction plays a substantial role as well. If you have essentially the same construction, smaller gauge strings will indeed result in lower tension. Were the lighter strings the same kind and brand?
"Flexibility" is also a well-defined physical quality. It's the inverse of stiffness, which is resistance to deformation—that is, the amount of displacement of a body given a particular force on it. The more displacement for the same force, the more flexible a body is. For a bass string, this will be a function of both tension and construction. Higher tension decreases flexibility (think "floppy B" because of insufficient tension), but again, construction matters. For example, for the same tension and all other things more or less equal, a round core string will usually have higher flexibility than a hex core string. So, again, same construction on both sets of strings?
Fresh-out-of-the-pack Slinkys are bright as anything but you don't have to play them very long for them to sound pretty dead. There's no difference in tension or stiffness, so I don't know where "tightness = deadness" comes from.