Differences -
Driver in Cloud 3 is 3mm bigger
Frequency response of Cloud 3 is 10 to 21 Khz wheres the Alpha starts at 15 to 21Khz (so cloud 3 can hear lower volumes than the Alpha)
Alpha headphones need more power to drive to higher volumes than the Cloud 3, sensitivity on Alpha is 103 compared to 111 on Cloud 3. Cloud 3 might seem louder in other words. Louder doesn't necessarily mean better.
Microphone on Alpha is bi directional whereas Cloud 3 is uni directional... (uni directional means it only moves one way (or could be it only picks up sound from one direction)) Both have noise cancelling.
Battery life on Alpha is up to 300 hours whereas cloud shows 120 hours.
Weights are difficult to compare as one website uses Metric and the other is US. Blames Google.
Everything else is more or less the same.
Cloud Alpha
HyperX Cloud Alpha Wireless features 300 hours of battery so you can game for weeks on a single charge and enjoy an immersive audio experience with DTS® Headphone:X® and HyperX 2nd Gen Dual Chamber Drivers.
au.hyperx.com
Cloud 3
The HyperX Cloud III Wireless gaming headset has up to 120 hours of battery, high-quality audio with 53mm angled drivers, comfortable memory foam ear pads, and clear communication with a 10mm mic.
hyperx.com
Cloud 3 are newer but from I can tell they don't sound as good. One person reported they sound flat and returned them after a week.
The main difference here is the price, the cloud 3 only costs $AUD279 whereas the Alpha costs $AUD319 so you get better sound and bigger battery for the price.
TO me, I would pay extra for the battery and sound.