Hand tied leaders, made from sections of monofilament material (tippet) knotted together...

PRO
1. Allow you to fine tune the leader design to meet special conditions, for example turning over really big bass bugs or casting into the wind.
2. Can be cheaper to make your own if you purchase the raw materials in bulk, pennies per leader.
3. You can add things like a bright colored section for a strike indicator or tags ends for droppers.
4. Knowledge acquired in building your own means you can make up what ever you need in the field if you are well stocked on tippet. Oop's, I left my 6X leaders at home, no problem I can build one right here.
5. You can mix and match materials, for example a butt section of stiff mono and a tip section of fast sinking flourocarbon.

CON
1. You have to tie lots of knots, takes more time.
2. Knots can collect debris if you fish water with lots of grass and weeds.
3. Knots can catch on your guides and are somewhat weaker than leaders w/o knots.

Commercial tapered leaders...

PRO
1. No knots, smooth continious tapered monofilament from butt to tip.
2. No assembly required, fast and easy for those that don't have extra time.
3. May have greater breaking strength due to fewer knots in the system, typically not an issue since the knot at the fly is probably your weakest link.

CON
1. Usually come in 7 1/2 foot or 9 foot lengths, what if you want a 12 foot leader for spooky fish or a short 4 ft. leader for streamers?
2. More expensive and getting more so over time.

Another option is to use home made (or commercial) furled leaders built of thread or monofilament. These are knotless tapered leaders built up of mutliple strands twisted together like a rope. They have great turn over power, are long lasting and inexpensive to make. Building them at home requires a simple jig and some comon tools you probaly already own. Use the search function on this web site for more info, there is a lot of stuff out there already.