JohnRob explained it but to polish the details just a bit:
The StackExchange circuit is just a proof concept and not practical, the peak applied voltage is limited to the Vgs rating of the mosfets and it can only drive a purely resistive load since there is no reverse current flow protection. This means pulsating dc output since you cannot hang a capacitor on the output to smooth it. This is what happens because you’re using the mosfets as switches. There is voltage drop with current flow due to the Rds rating of the mosfets.
The LT4320 actively controls the gates of the mosfets, elimating the reverse current flow allowing a capacitor for smoothing on the output. Why would you want an ideal rectifier? From the AD website:
Analog Devices’ ideal diode bridge controllers replace the four diodes in a full-wave bridge rectifier with a low loss MOSFET to drastically reduce power dissipation, heat generation, and voltage drop. The Schottky diode bridge rectifier is a classic circuit used for full-wave ac-to-dc rectification and dc polarity correction. Due to the ~0.6 V drop of each diode, the two diodes in the I/O path dissipate power (1.2 W per ampere), radiate heat, raise the ambient temperature, and complicate thermal design. At low input voltages, the two diode drops significantly reduce the voltage available to the downstream dc-to-dc converter. Ideal diode bridges eliminate or reduce heat sinking requirements, which helps shrink the overall footprint and provides significant cost savings.