Compressors & multi-band compressors are both handy tools & serve their place in the mix.

Regular compressors will reduce the entire signal as a whole; whereas multi-band compressors will target & compress certain frequency areas.

Usually, a regular compressor is perfect for the job when the goal is to control the dynamic range.

Situations, where you may use a regular compress, would be when you need the entire signal compressed down like the entire mix bus, a drum sum, a lead vocal, or a dynamic bassline.

You can still use a multi-band compressor later on in your chain. You can definitely use both. It doesn't have to be one or the other.

Situations, where you may want to use a multi-band compressor, is when you need to reduce resonance, harshness, or buildup in a certain area.

Maybe a vocal has a little boxiness in the low-mids & some harshness in the upper-mids. Your mix bus may need a little rounding out in the low end & some reduction in highs.

Maybe you have a pad that's not very dynamic, but there's a little bump in the mid-range that's conflicting with the rest of the mix. Multi-band compressors are perfect for this.

Multi-band compressors also work great for side-chain compression.

Especially when it comes to balancing 808s & kicks.