I have to first confess that I am old school, when I first started in the pool industry Concrete was the dominant pool. Things have changed over the years and the options are many now all have their advantages and disadvantages. Here in, the best non-biased format I can muster is my opinion of the choices you list.
CONCRETE ADVANTAGES- This pool if built by a reputable builder will last several generations. The surface of the pool, if the water chemistry is well maintained will last for many years. I have seen a 25-year-old concrete pool that was in mint condition, it just needed an acid washing to bring back the dull color. This pool just looks great and you are not limited to what size or shape you want. The sky is the limit to what you can build. There are some pretty impressive concrete pools being built these days.
CONCRETE DISADVANTAGE- the price, depending on where you live, can be steep. If you are in a northern climate frost heaving can be a problem with the tiles in older pools. After a number of years the pool will have to be acid washed to bring back the bright white color of the plaster if you choose a white plaster finish. Acid washing tends to rough up the surface and after awhile it will begin to cut the feet. To solve this problem you will either have to resurface (expensive or paint, once you start painting you will be painting every 2-5 years depending on the type of paint you use.)
FIBERGLASS ADVANTAGE- This pool is easy to install so it makes it less expensive in most areas than a concrete pool. The surface is smooth and easy on the feet. They have done some great things in recent years with fiberglass pools and you can really dress them up. The pool is easy to maintain.
FIBERGLASS DISADVANTAGE-You are limited in size and form. The size of pool they make is limited to how big they can transport on the back of a truck, usually in the 14' wide range. Shapes vary from manufacture to manufacture and there are quite a few choices compared to 20 years ago. The surface of the pool is smooth and can be slick on the steps creating a slip hazard. If you are installing the pool in a sandy area it can tend to shift over a few years and then need to be reset. If you do not maintain the chemistry properly the pool surface can be ruined and the pool would have to be replaced or re-gel coated.
Well there you have it as un-biased as I can make it. I am sure there are some points I may have missed, but I believe I have hit the major points. I hope this helps everyone with their decision making process.
Guru of Pools