Would a relatively small black hole attract objects in a different way than supermassive ones?
Small black holes are less massive than large ones and therefore exert less force on objects. When you are a reasonable distance from a black hole (say, more than 100 Schwarzschild radii away), the Newtonian formula $F=GMm/r^2$ is a good approximation.
On the other hand, as you get close to the event horizon, the spaghettification effect from the gravitational gradient will be worse for the smaller black holes.
No not really. The only force acting here is the force of gravity. So, a black hole cannot attract objects differently because of its size. The only disceprancy however is in the size of its event horizon and its acretion disc. A bigger black hole can capture objects that are more farther away than smaller black holes can. And i do not believe that inside a black holes acretion disc, the gravitational force varies due to its size. At this point, the spacetime curvature is infinite. There is no measurement of variables in infinity. atleast, None that we know of. So, basically, bigger black holes just have a wider vacuum cleaner than smaller ones, but they all have the same power. Loosely speaking.