Vanish has been improved in the last few years, but it's still not a very good fluoro (and that's coming from a Berkley fan). I really like their 100% fluoro as it's less brittle and manages well. The differences between Vanish and a mono are their water absorption, their sensitivity, abrasion resistance, and how they act in the water.
Fluoro doesn't absorb water so it's characteristics stay consistent throughout the day. Mono in general will absorb water and when it does it becomes a little more stretchy.
Fluoro is made out of a more dense material so not only does it sink in the water column, but it also transmits vibrations better and in my opinion creates a more sensitive line. For the same reason, I feel it helps transmit bites better for semi-slack line presentations such as wacky rigging.
When it comes to abrasion resistance between the two, I feel there's a trade off. In a mono, there isn't as much abrasion resistance, but to me it doesn't seem to lose as much strength if it is nicked. Fluoro is more abrasion resistant, but when it does get a nick in it, it seem to lose strength a bit quicker than a mono.
As far as how they act in the water, like I mentioned mono floats in most cases, where fluoro sinks. Although the two lines have somewhat similar stretch rates, I think this is why people don't feel that fluoro stretches as much. With mono the line is almost always wanting to rise up in the water column creating somewhat of a bow in your line under water. When you set the hook you're overcoming the slack in the line and pulling it tight and then the line stretches. With fluoro I think the line keeps a more direct path to the bait so when you set the hook with that you only feel the line itself stretch.
Above are my observations from using both mono and fluoro. Both are good lines and have their place in the fishing arsenal. If I were you I'd venture away from Vanish and at least step up to 100% Pro Grade. If you're worried about the cost difference, I intentionally left the same line on one of my most heavily used rods for two years just to see if it broke down over time. If it did I didn't notice any loss of performance, and still had zero issues with it. If I had to choose between vanish and XT or XL I'd choose either of those mono's before Vanish but to each his own. Figure out what you like and what works for you!