Many popular models of high-end tripods or mono-pods are available with both aluminum and carbon fiber legs. I struggled to decide which to go with when I purchased my tripod and I wanted to present some thoughts on the advantages / disadvantages for each.
In my opinion, Carbon Fiber tripod offer only one real advantage to their aluminum counterparts, and that is lower weight. Carbon composite construction offers a higher strength to weight ratio compared to plain aluminum tubing and this allows tripod manufacturers to make a tripod with comparable dimensions and loading capabilities that weighs less.
The question then becomes, how much is it worth to you to save some weight? If you are hiking to your photo location then it very well may be worth the extra money to lighten your load.
The weight savings is not worth it to everyone though. In my situation, I was expecting to use this in the field sometimes, but I didn't expect that I would be hiking very far to the locations. I was close on budget because of the need to purchase a ballhead and decided to forgo the carbon option.
If you plan on using your tripod solely in a studio type setting, then there is really no need to worry about the weight of your tripod. If anything, a heavier option may make the setup more stable.
Whenever the advantages to a carbon fiber tripod are listed, vibration reduction is inevitably mentioned, especially by the manufacturer of said tripod or by the salesperson trying to get your cash.
The concept is that carbon composite construction offers a quality where vibrations are reduced in the system and that this will allow sharper photographs. There are a few different corollaries that can be made to the comparison between carbon fiber and aluminum construction. One is a simple observation that different materials do indeed transmit energy differently. If you take a wooden dowel and whack it on a table, then do the same with a metal pipe, the sensation will be different. The sound will be deadened from wood compared to a harsh ringing from the pipe. There are other examples of carbon vs aluminum construction in sports equipment. Anyone who has used an aluminum vs a carbon fiber tennis racket can attest to a difference in feel and a reduction in vibration while using the carbon product. The same goes for bicycles, where a carbon fiber frame will absorb some of the vibrations from small road discontinuities where an aluminum frame will pass them on to the rider. All are cases where the energy is dissipated internally instead of being transferred.
So it is reasonable to understand the inherent differences in how the two materials transmit energy. The real question is if this characteristic can relate to the system of a camera / tripod interface and result in sharper images.
Let's discuss what are the sources of vibration in the camera/tripod system: mirror flap, contact between the operator and the camera (hand, face, etc.), wind, vibrations from the ground. You first need to realize that only certain photographic situations will be affected by vibrations; namely, shooting at slow or extended shutter speeds. If you find yourself shooting in these slow shutter speed conditions, a good photographer will take action to eliminate as many sources of vibration though good technique. These include using a remote shutter release (eliminates your face and hand as a source of vibration), setting the mirror up (eliminates mirror flap), adding secure weight to the bottom of the tripod (adding mass to the system can help reduce buffeting by the wind). All of these techniques are free and can greatly decrease vibration and help your images become sharper.
It is possible that the above sources of vibration could be reduced, in theory, by the properties of carbon composite construction. However, this improvement is so small as to be inconsequential compared to other methods of stabilizing the system and will prove to be unqualifiable. Bottom line: I have yet to hear of an established professional photographer point out that the sharpness of their images can be attributed to using a carbon fiber tripod. There are some studies and test that work to prove this effect and improvement, but be warned that there is often a large disconnect between test results in a lab and actual improvement in the craft that is photography.
If the point of getting a carbon fiber tripod is to save weight as you travel to your photo site, it is important to not carry excess with you; otherwise, your extraneous gear will negate the savings you paid so much for with your fancy tripod.
More specific advice would relate to the choice of head that you pair with the tripod. If lightweight is the goal, resist the temptation to purchase a ballhead that is above the capacity you need. Heads with higher loading capabilities are larger and weigh more.
As an example, let's look at two setups. The first is a Gitzo GT2331; a cost efficient aluminum model with a center column and three leg sections. It weighs 1,957 grams. Let's pair with with a Really Right Stuff BH-40 LR (lever release) ball head. It has a capacity that matches this tripod, and has a weight of 479 grams.
The second setup is a Gitzo GT2830. It is similar to the first setup as it has center column and three leg sections, but it has carbon fiber legs and a lower weight of 1,547 grams. Let's say this is setup with an overkill ballhead, the RRS BH-55 LR. This ballhead weighs 862 grams.
The total weight of setup one is 2,436 grams and the total weight of setup two is 2,409. The weight savings that were so costly in the carbon fiber tripod were eliminated through a selection of a heavy ballhead.
Just to be clear, there is no inherent performance penalty for choosing a carbon fiber tripod. They can be designed with loading capabilities that are equal to aluminum counterparts. If weight is a concern or you simply want high-tech equipment, a carbon fiber tripod can be a great purchase.
If you are on a budget and want the best value for your buck and are willing to tote a bit more weight, aluminum is your best choice as a tripod material.