Dragoon - Crit, DET, or Skill Speed?

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If I have the max crit chance I can possibly get, will my crits be doing more damage than if I were to have stacked determination and have an extremely low crit chance.

I went ahead and pulled this quote out to kind of help you understand the bigger picture of how this works.
The amount of damage output you do overtime takes into consideration your determination, your critical hit rate, and your skill speed, no matter whether you stack one or the other. Fortunately / Unfortunately in FFXIV, the actual gear customization you can choose is very little. When you get the max critical you can, you won't be lowering your determination really all that much, and vice versa. Let me find the BLM graph someone linked to help you kind of visualize this.

http://i.imgur.com/KvihQt0.jpg source: https://docs.google.com/spreadsheet/...TDVkM1E#gid=50

You can see that it is for black mages, and they have different stat weights. But take note that there is very little change in the amount of damage being done based on whether someone stacks something or not. The same big idea applies here for dragoons.

But really, the best way to answer your question is to use math to determine the values (which we have listed here for you.) If you were to ask me to explain to you in a couple of sentences how to determine stats for your dragoon, I would say it like this:

Stack strength, then determination because it is worth about 1/3rd of strength. Critical hit is worth about half of your determination, and skill speed is worth a little bit less than that.

To further explain this, let's say you're fighting a monster for 60 seconds. That gives you something like 24 attacks. If you have a 15% critical rate, 3-4 of those attacks (excluding dot ticks) and your auto attacks are going to critically hit. If you have 20% critical hit rate, 6 of your attacks are likely to critically hit. I think the highest I've ever seen posted on this forum from a parser is a guy who super stacked crit at the expense of ever strength and he managed to only hit about 25% critical rate. So let's say you're stacking determination with lower crit, down to even 10% critical hit. That means about 2-3 of your attacks are likely to critically hit. However, when stacking determination, those other 20 attacks are all guaranteed to do more damage. According to all of these guys who have been mathing it out for a while, they suggest that determination actually increases your damage by a significantly larger amount than upping your critical hit rate would, for a dragoon. Once you move on from 24 attacks to something like 100 attacks, the numbers start to even out and because even more obvious.