There is 2 major concerns regarding strings: its tone and its feel.
A string can feel more stiff or soft if you use action higher or lower. This relates on how hard you're used to play (how strong you touch strings) and how you need strings to react to your finger. This also affects our speed and tone, since they can buzz more.
Using a lighter set can make a string feel softer (or floppier, if you don't feel confortable with that) or stiffer (or hard, if your touch is light), in same fashion and same results described above. In fact, you can cross match those 2 factors: Action and Gauge. Sometimes fret noise (string buzz) prevents lowering string action without thiken strings, compensating string floppiness on low action with heavier (and stiffer) sets.
All this can affect your confort, speed and tone while playing regardless brand or kind. This is my main reason to master bass setup on my own, since any changes on string demands adjustments on bridge and truss rod to keep bass feel as I am used to.
But there is other factors.
Some say hex core make strings stiffer compared to round core, I can't confirm that since I don't remember using round core strings. One thing seems to be clearer to most people, though: steel and nickel feels different. Steels seems to be more agressive on finger and frets than nickel strings, but this starts to affect tone.