Question
hi, can you please tell me what are the pros and cons in using compost boxes?  

Answer
You do not need a special container to compost, atleast you do not need to buy special expensive containers.

You get same action from using a roll of 3 foot wide chickwire rolled out and stapled together into a ring. Fill the ring with compost. This is a $9.95 investment at home depot and is just as good as a $295 compost container available online or at garden centers.

One of the benefits of a compost container is that compost sometimes is easier to turn. One of the ways to speed up composting is to "turn the pile" often (e.g. mix up the layers so air is re-introduced in the pile and partially decomposed pieces are mixed with uncomposted pieces).

Some purchased containers (such as drums with handles, etc) allow for easy turning which then means that you do it frequently. You can also turn compost with a chicken wire setup as above. All you have to do is to unsnap the staples (I use twist ties) and then remove the ring from the compost. Re-snap the staples (or re-tie the twist ties) and recreate the ring. Place the ring to the side of the pile and shovel the compost back into the ring. It takes a few minutes and some arm strength, but it is just as effective.

A formal box (or even a chickenwire ring) also have the benefit of keeping compost enclosed so that it does not fall apart or blow away. Some compost boxes also protect the compost from excessive rain (I place my chicken wire ring under mature oak trees to allow for some moisture but not a lot).

A formal box may also be able to discourage rodents from digging your compost. A chickenwire ring would make it possible for animals such as squirrels, field mice and cats to get to your compost.

There are pros and cons using compost boxes. Primarily the cons are the prices and also (often) the limited storage capacity. In many instances, you can get the same benefits from a simple sheet of chicken wire wrapped together in a circle and tied with twist ties. A chicken wire ring is still not as easy to turn as a drum with handle. It will also not protect as well against animals as an enclosed plastic box.

In the end, it is your choice.

The compost that comes out in the end is no different using a chicken wire (or even letting the compost rot in a pile) vs using a store bought box.