The sensor technology out of the way, Microsoft's Explorer Mouse becomes a less relevant comparison to the Performance Mouse MX. Both are wireless devices, and both offer battery recharging, but the Explorer Mouse has a much less ambitious take on those features than the Performance Mouse MX.
For its wireless technology, Logitech has brought the Performance Mouse MX into its Unifying USB microreceiver family of devices. The microreceiver itself is a tiny nub of a thing that sticks out less than inch from a typical USB port. As a member of the Unifying family, the Performance Mouse MX can work in conjunction with six other Logitech input devices on the same receiver. Granted that means you're tied to those six devices to take advantage of that efficient receiver ecosystem, which means spending more money on new products to get the full benefit of the Unifying technology. If you're in the market for a complete input device overhaul, we can at least recommend the one Unifying keyboard we've reviewed so far.
For its part, Microsoft's mouse relies on a standard USB receiver that works with only the mouse it was purchased with. The receiver does snap into the body of the mouse for easy travel, but with the Logitech's microreceiver design, the receiver is so small you don't need to take it out of the USB port to begin with.
Logitech also has an advantage in its recharging design. There's no great magic here. Rather than a recharging station, as Logitech has used in the past, it's simply added a mini USB input into the front of the mouse. Connect the mouse to a powered USB port via the included cable and you can recharge with no usability downtime. While this design does require you to keep track of the cable (or find a full USB-to-mini-USB cable somewhere), we much prefer it to the clunky recharging station that Logitech has used in the past (and that Microsoft still uses, in trimmed-down form) that prevents you from working while your mouse re-energizes.