I can only give you my own personal experiences with these tests!
I was diagnosed with congestive heart failure and severe mitral regurgitation via an echocardiogram in the fall of 2003. My cardiologist referred me for a cardiac catheritization.
The echo showed the valve problem clearly enough, but one reason the cardio wanted the cath was to see if there was anything else going on. Cardiac cath is, I was told, the best way to find out if you have anything like blocked arteries. I asked if there was anything less invasive that I could do instead. I was told there are, but that for what my cardio wanted to know, there is nothing as good.
Luckily, my arteries turned out to be (in the words of the cath doctor), "pristine." Which was very good to know when I went in for the mitral valve surgery!
Don't be too worried about the cardiac cath procedure. I was really freaked ahead of time by having to go in for it, but it turned out to be a really easy test for me and I think for most people. The only thing I ever felt was the prick of the needle with the local anesthetic; after that you really feel nothing. You are usually well tranquillized but they don't want you unconscious. I was really scared & asked for more tranquillizer and they obliged.
The worst part of the procedure itself, for me, is that the cath lab where they actually do the procedure is kept VERY COLD. They'll give you a blanket but be sure to remind them! The worst part after the procedure is that you usually have to lie on your back (with a weight on your groin area to avoid bleeding) for some time. (I had to stay six hours.) You can't sit up so you can't read; so take an iPod or something so you have something to listen to. If you get really antsy during that time, and the tranks from the procedure wear off, they'll probably give you more if you ask, so you can sleep. (If you can sleep on your back, which I have trouble doing.)
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About the TEE: I didn't have a TEE before the surgery. Or rather, I know I had one but it was when I was already anesthetized for the surgery, so I didn't know about it.
I did have one when I was conscious, but that was several months after the surgery, during one of my check ups. I say "conscious," but not really. When you go in, the first thing they do is to give you a sedative intravenously. By the time you get to the TEE lab you are pretty close to comatose! They spray your throat with a substance to prevent the gag reflex and then they stick a tube down your throat. Sounds awful but by then you are so numbed with the sedative and the anti-gag-reflex spray that you absolutely don't mind anything. The only bad part is a few seconds while they are spraying your throat -- what they use tastes pretty bad. The sedative they use (I have forgotten what it's called) also has an amnesiac effect, so you don't remember too much later. Afterwards you aren't supposed to eat or drink for at least two hours, until the anti-gag-reflex stuff wears off.
