Well Dana, let me help...
OC Trimix is the most expensive class I teach. I almost never teach it because I feel like the student is getting ripped off.
A few years ago I co-taught a class with a buddy of mine. We spent a week diving Eagle's Nest Cave (300' deep). At the end of the week the two students had spent $1700 on gas fills. Had they been on a rebreather, they'd have spent less than 10% of that.
I guess if cost is the deciding factor, it would depend on how many deep dives you plan on doing. For me, the last 10 dives I did were all 5+ hour long and 300' deep. So, it adds up quickly. But even if everything were equal, and cost didn't play into it at all, it'd still be worth it to fork out the cash and dive a CCR.
So when you are trying to talk your wife into it... here's the bullet points. While they may or may not be 100% factual. They are close, and they make a good argument.
Diving a Rebreather is safer. Especially if you area a cave diver doing deep dives. Imagine, between the rebreather, dive buddy, and your multiple options for bailout, you literally have 3 or 4 completely independent options for survival.
Diving a rebreather is lighter, considerably. My 104's weighed 140lbs fully rigged. My rebreather (on the heavy side is 70lbs). Some rebreathers are under 50. This means your back is going to last longer. Your ankles and knees too. That means you can do yard work well into your 70's.
Diving a rebreather is cheaper. If someone calls me up tomorrow and says, "Hey, you wanna go dive Eagle's Nest?" I don't have to fret. I've already got the bailout, and it costs just $26 to fill the sorb, o2 and diluent to make a 5 hour dive. That's a no brainer. I don't have to cough up $300 anymore in open circuit gas. Woohoo.
If you are into wreck penetration or cave diving, a rebreather is safer because you have virtually unlimited time to get yourself out. My rebreather is good for 10+ hours. Make a wrong turn, get lost, silt out. Lights die, tangled, collapse.... I've got time to fix it.
And between me and you, if all of the above were equal, from OC to CCR. It'd still be worth it just by the fact that I don't have to look at a pressure gauge ever again during a dive.
Once you get used to diving the right rebreather, there's nothing better for diving enjoyment. And you just won't understand until you buy one and hit about 25 hours on it.
---------- Post added October 18th, 2015 at 12:13 AM ----------
Also I should say (back to your original question) that if you have a BoV (Bail Out Valve) on your rebreather, which is just a DSV that doubles as a second stage regulator (plumbed to bailout gas usually), you need only flip a lever to bailout. This switches your gas from the loop to a fresh supply. It's quicker, and ultimately, probably safer, but does cost a butt ton (metric not imperial butt ton) and sacrifices some Work of Breathing.