I had a key lime that ended up getting a fungal problem, but it was a reasonably tolerant tree for the years I had it. The same problem attacked my plumeria too, and they survived with treatment. It was just too late for the lime. It would drop leaves when I moved it inside/outside with the seasons, and it took me a while to realize that there was a reason for that final leaf drop.

I would have gotten another one, except I heard that key limes need more heat to set fruit than a Persian lime. I can't guarantee the summers here (and less other times of the year) in Colorado will get as hot as citrus would want. I am really quite disappointed because I hear they are prolific and vigorous trees.

Historically limes originated in SE Asia many millions of years ago. They have mostly been propagated in other parts of the world by humans.

Key lime is synonymous with Mexican lime. They are small fruited and usually picked unripe (green) for a sour taste.

Persian lime is synonymous with Tahitian lime and is larger fruited. The cultivar Bearss is typically sold in the nursery trade. It is excellent for culinary use. The cold tolerance is about equivalent to Mandarins in my experience.

There are several other species and cultivars of limes, for example Kaffir lime whose leaves and zest are used in Thai cooking (the fruit is insipid).

To control fungal infections on Citrus I recommend a copper fungicide; for example Liqui-Cop or Kocide 3000.

Here is a link that might be useful: Principal Lime Varieties

Greendreamhome, I am going to make an assumption that because you are living in AZ and in zone 9 like myself that you are going to be planting you tree in ground. With that said, I have both a key lime and a Bearss (Persian) line tree. My key lime tree produces year round, it is very very prolific and I barely give it any attention other than water and fertilizer a couple times per year. My bearss lime tree also produces well but is still young and does not produce as much as my key lime. The limes on the bearss are a little larger but not by much. As for frost sensitivity of the key lime tree, I had temps down to the mid 20's over the Christmas week with absolutely no damage to It and minimal damage to my bearss lime (it had some fresh growth that hadn't hardened over yet that was nipped by the cold temps). So in my opinion either tree is a good choice for a home garden but be prepared to give away half of your key limes because of how many it will eventually produce.
Here is a picture of my key lime tree.

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As you can see below it, I picked as any limes as I could and I still have some falling off sitting on the ground.

This is my bearss lime tree.
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As you can see a much younger tree, but it will be producing much more this season as it is in its second year in ground. Best of luck and let us know what you decide to do!

Evan

Oh I forgot to mention, they do make a thornless key lime/ Mexican lime, if you can find one of those, if that's what you decide to plant, I would do so. The regular key lime tree is very thorny, the bearss is thornless.
Evan

They also have a giant key lime. Just ordered one but I'm only giving it a 50/50 of surviving shipping as its in the 20's outside but the mail gets dropped off at the office.

I have both in my greenhouse and love each of them. The key lime is a larger tree and always seems to have some sort of pest but it is so productive - I think it has fruit on it all 12 months of the year. Though the fruit is smaller it is very juicy. My Bearss Lime has a lot of fruit also and when fresh picked they are better than anything store bought. This tree doesn't suffer too much with bugs and though it is not as productive as the Key Lime it still produces more fruit than I can use. My favorite thing about it is the way the tree smells, mostly when you brush against it - like a Dairy Queen Limeade. They are both worth growing in my book and the Key Lime is far hardier than anything I've ever read about it.

I have both too. I'm considering removing the bearss because its just to normal. I can get them whenever I need from the store, the quality is better from my tree but its just not enough to keep. I am more focused on rare and unusual citrus/tropical. Even though key limes are somewhat usual they are very seasonal in my area and the tree & fruit quality are far far above store bought.

As far as vigor, the key lime has been very trouble free very productive and very vigorous. I have to prune this one a few times a year. The one thing I noticed is its fruit load is very dependent on amount of direct sun. I moved it to a 1/2 day shade and it produced about half of the amount it did the year prior, its possible its just an off year though. Mine is a cutting - not grafted. They are some of the most sensitive citrus to frost.