On eBay there are cheap ceramic vegetable peelers like this:
Do they work well? Right now I have a simple, knife-like peeler with a hole in the middle which I hate and I'd like to change. Does this type work better?
Yes: I find they work very well on easy-peeling vegetables; for example on nice straight carrots or parsnips, I can trim a very thin peel easily and consistently.
No: But on more difficult vegetables, they aren't very good at dealing with tougher or rougher skin. For example on jerusalem artichokes or knobbly potatoes which need eyes removing, they fail miserably.
For a good all-round peeler, I use either a Lancashire (fixed-blade) or Jonas-style (in-line swivel-blade):
The difference between that and what you already have is really just the position of the blade with respect to the handle. With that, you pull along the direction of the handle to peel, while with your current one, you push perpendicular to the handle. (Assuming I understood your description of your current peeler right, anyway.) Which of the two you prefer may be mostly personal preference, though I find that the angle you end up holding your hands at is nicer when you're pushing perpendicular.
You haven't said why you hate your current one, but I'm guessing it's because it's dull, and possibly uncomfortable to grip the handle in order to exert the force you need. (Note that it takes more force when it's dull.)
So your problem may well be solved simply by getting a new, sharper peeler, preferably one with a handle you find comfortable to hold. I'd suggest going to a physical store and actually holding them to get an idea of what you like.
Ceramic vs metal blades is a factor too, of course - ceramic holds the edge better. But I'd worry first about getting something comfortable to use. Better to have something comfortable to hold that has to be replaced a little more often than a nice sharp ceramic blade attached to a handle you hate.
How deep a peeler cuts into vegetable matter depends on how big the gap is between the two blades. If you're used to a narrow blade spacing, and switch to a wider one, you'll be horrified at the depth of the peel, Conversely, if you're peeling for stir-fry, a wide spacing, thick peelings, might be preferable.
So whether the pictured ceramic vegetable peeler will work well for you will depend on what its blade spacing is, and what blade spacing you're used to having.
I find them horrible. The wobbly top doesn't allow to put any pressure and instead of cutting into the vegetable, it flips and scrapes it or slides. The theory that it will follow the shape of the surface is flawed - to get it to sink under the skin you have to push and the flimsy construction feels like it were to snap. Also, the angle is good only for biggest vegetables, you'd have a hard time trying to peel a smaller potato, and with softer vegetables the required pressure will squeeze them. If you try to peel a raw carrot, the blade will catch, flip and then scrape instead of cutting. If you peel a boiled one, it will drag the skin or just snap the carrot if you press harder, to cut.
vincebowdren suggests a better model, the blade is fixed to the handle, at an easy to use angle (the fact the blade is perpendicular like in a shaving razor, is a marketing trick to suggest it works as well as one; it doesn't, trust me.) You can control the angle and pressure better, and it only maintains cutting depth, plus the tip is great for picking out "eyes" out of potatoes and the like.
That type of vegetable peeler can be very effective. A lot is going to depend on the sharpness of the blade, so it will vary from brand to brand. The Kuhn Rikon peelers of that style (with steel blades) have a very good reputation. I have personally used them to do everything from peeling vegetables (carrots, potatoes, eggplant) to making Parmesan shavings, and it worked beautifully for all of the tasks.
They do work well. As far as ceramic vs metal blades go, ceramic will last longer. But giving the general cheap price it does not really matter.
As an alternative I find these the best and easiest to use:
They have the point on the end for removing holes/knobs etc.
And they shouldn't run you more than a few dollars.
Which is better? Its very subjective and depends whats easiest for you personally. I prefer the straight type peeler. I've tried the perpendicular ones and I find that I'm only able to do short sections of peeling at a time with it since it knocks against my fingers of the hand im holding the veg with. No such issue with the straight one, I can do long sections of peel quickly. (Try peeling a whole apple or potato in one long piece with the other type!) Every time i see someone using the perpendicular type, they are so slooooow. With a straight one i can get 3 times as much done in the same time. I'll challenge anyone to peel quicker than me if they are using a perpendicular one !! This is my own peeler which I have had for about 10 years. Still sharp and the little point on the end is good for digging eyes out of potatoes etc. But like i said, it all comes down to preference. Try both and compare, see what you like best.