Higher stats absolutely have a noticeable effect. Just look at your numbers when swapping gear around. Every Job gets noticeable effects from the various secondary stats. You need large amounts of them to get anywhere, which would be an issue if we weren't getting them by the hundreds right now.
Determination brings a very noticeable degree of consistency to your output.
Critical Hit Rate brings a very noticeable increase in the frequency of critical hits.
Skill/Spell Speed brings a very noticeable change in how quickly your gcd spins.
Every Job gets these benefits. The thing is that every Job gets different bonuses from each of them, based upon what their optimal rotations look like and (in some cases) how the stats interact with their skills.