Generally, the light is softer and less directional (sounds funny, since you can 'aim' them) from a soft box than from a white umbrella ... like diffused light coming in a window. Great for people, in many cases, but for pet fur to stand out you can't have too soft of light. I've even used silver 'brollies' but they tend to sharpen the shadows a bit too much for me.
You can make anything work just fine ... so start with either what you have, or the cheapest setup if you're just buying stuff. You can always use what you buy for something!