There's a reasonable difference. 'Noticing' is subjective so difficult to say, but it's certainly plausible that some people will notice. It's not as big a difference as the difference between an HDD and an SDD.
Put another way, it's not worth upgrading a motherboard for, if your motherboard only supports SATA II. Or if the SATA II SSD is significantly cheaper, it's might not be worth paying the extra money for a SATA III SSD, but then again it depends on what's important to you.