Adding the front diffusion cover generally makes the light less efficient but more controlled.

Compared with the bare reflective umbrella, the covered setup will usually:

• Transmit less light to the subject, so you’ll need more flash power or a wider aperture. A rough estimate is about 1 stop, though it could be closer to 2 stops depending on the cover and setup.
• Produce softer, more even light because the diffusion panel spreads and smooths the light.
• Reduce hot spots and make the output look more uniform across the front of the modifier.
• Give gentler falloff than the bare reflective umbrella.

The exact difference depends on variables such as the umbrella’s size and shape, the flash power, the type of diffusion cover, and how far the modifier is from the subject. In short: without the cover = brighter and punchier; with the cover = dimmer, softer, and more even.