If you've been on SFMM's Revolution, you can see the difference right there in one ride.
The second hill is a parabola and the drop leading into the loop is a circle-and-line (on the "down" side, anyway)
Parabolic hills have continually changing curve radii (like a clothoid loop does) while C&L hills have a curve, straight line, curve, straight line (like a flat track leading to a circular loop).
Let's look at it in No Limits:
A parabolic hill (and we're starting on the ground here, approaching the hill) has a continuous curving action up to a point somewhere on the rise of the hill. At this point, the upward curve reverses into the curve that turns into the top of the hill and there is a continuous curve over the top to a point on the down side of the hill. At that point, the curve reverses again into the pull-out of the hill.
The main thing is that the track is continually in a state of curve, either curving into the hill or out of it.
The C&L hill curves into a point fairly low on the up side of the hill, then there is a section of straight track at a constant angle leading to the top of the hill. There, it begins another curving section to get over the top. It's important to note that this curved section is a part of a circle rather than an arc with a continually changing radius. Once over the top, there's another piece of flat track at a constant angle of descent that leads to a piece of a circle to exit the drop.
The difference in the ride is dramatic. Parabolic rides are generally more comfortable and can offer a wide variety of kinds of airtime. They can be engineered for floats, ejector, or combinations of those. In that first hill, you'd experience some positive Gs leading to the midpoint of the upside, then you'd gradually begin to feel fewer and fewer Gs until the crest of the hill, where you'd float over the top and halfway down the other side until the curve reversed, then you'd come back down and the Gs would gradually increase as you approached the bottom. Most (if not all) modern coasters are built this way.
On the second hill, you'd have strong Gs at the base of the hill, then would go back to around 1G on the flat track heading up. When the flat track meets the circle, you'd get a strong spike of negative G and would have ejector air. IF the train is going fast enough, you'd remain out of your seat all the way over the top and would get slammed back down pretty strongly on the flat track going down. If the train isn't moving that quickly, you'd get the ejector spike, then ride over the top, then get another ejector spike when the curve met the straight track again (at least in the back car).
In my experience, I like both kinds, but the ability to enjoy a C&L design has a LOT to do with the comfort of the trains. You need lots of padding and a lap bar system that won't kill your thighs when you get ejector pops.
The original version of Mexico's La Montaña Rusa is perhaps the biggest and most extreme C&L design I can think of that I've been on. It was terrifying and brutal. It also had wonderful NAD trains with buzz bars, which was the only thing that kept you from leaving the exit platform with a broken spine and cracked femurs.