A biquad is an IIR implementation so I do not know how it differs from "regular PEQ IIR" filters. Biquads are easy to implement (in several forms) and have fairly simple terms (since it's a biquadratic equation) making it easy to port among different DSP systems. Cascaded biquads are often used for higher-order filters, mimicking old-school analog filter designs.
To answer your question I'd need to know what you are calling a "regular PEQ IIR filter" topology.
The bigger question might be why use IIR instead of FIR filters or vice versa, but it's been a long time since my filter days. Simplistically, IIR filters tend to be low-order but fast (minimal latency) and low in complexity (simpler, cheaper, lower in power to implement). They are not generally constant phase/group delay so can distort pulses, not usually a big deal for audio. They usually roll off faster for given filter order compared to FIR filters, but are not guaranteed to be stable so higher orders are more challenging. FIR filters are slower (higher latency), complicated, and consume more power, but their many taps means very high order can be achieved (fast roll-off), generally have linear phase and thus constant group delay so better pulse integrity (not always a big deal for audio), and are always stable. Linear phase (constant group delay) and stability, along with copious computational power available, makes FIR filters the choice for many audio applications. But I have often seen cases where digital crossovers are IIR and room correction filters are FIR in the same processor. And of course various DACs may allow you to choose one or the other or a combination.
Things like the miniDSP units, using smaller DSP chips, can handle more IIR filters than the many more taps (multipliers) needed for FIR filters. I do not know about miniDSP specifically, but it was not uncommon in my work to add an all-pass filter after IIR stages to correct the phase when needed. The all-pass filters could get tricky, natch...
