MBR vs GPT (which technically has a MBR, although not used for accessing partitions) isn't a property of the disk, but something you can choose when recreating the partition table
Now, MBR partition start positions and sizes are limited to 4 tera-sectors: almost every disk for tens of years used half-kB sectors, therefore the 2 TB limit
Then, "recently", disk companies started increasing sector sizes (to reduce "wasted" space on the actual platters, used for tracking, error correction, and stuff): this is called "Advanced format" but of course, tons of implementations assuming there would never be sectors different than 512 B resulted in most implementations still emulating said sector size, therefore requiring some care for best performance (the exact same argument of partition alignment on SSDs)
Further later, Advanced format disks with logical 4 KB sectors were made - these would actually allow for 16 TB with MBR, however I would doubt their compatibility with PS3 or even PS4 - they're maybe 6 years old by now, but still a niche products (most integrated sata controllers made today don't support them, etc)