The tire shop where I take my flat tire to always patches them on the inside
then they re-spin balance them. I remember when you could buy a 7.50 X 14
Goodyear whitewall tire for what they charge to patch/repair.

Because they are lazy.

Unless you have no other choice and need to get rolling again, always
patch instead of plug.  
------------
Alex

Always plug the hole, never patch from the inside.  

Reason:  When you fill the hole with a properly installed rubber-fibre
plug, the repair vulcanizes to the surrounding tread and plies.  The plug
therefore restores the full thickness integrity of the tire.
An inside patch, on the other hand, leaves the hole open and the tire
vulnerable to a repeat puncture.  Any foreign object can enter the hole and
penetrate the thin membrane patch on the inside, puncturing it and allowing
the release of air pressure.  You can test this theory with a small
screwdriver.  Just push the blade into the hole and through the patch.  You
cannot do this with a plug because the plug is as tough as an unblemished
area of the tire.  Try it!

Tips:  I recommend the type of plug which is rubber-fibre in composition.
Clean out the hole with the roughing probe and THOROUGHLY LUBRICATE THE
PLUG with cold-vulcanizing tire rubber cement before you force the plug in
with the installation tool.  Then withdraw the tool.  The finished plug
should have doubled over on itself with both ends of the plug showing about
1/4 inch on the outside.  Trim to flush with a razor blade.  When plugs are
installed without cement, they often seep air and for that reason, plugs
have developed a bad reputation.  I never have trouble with plugs installed
with the cement  which acts as a perfect sealer.

Patch is much better. Just don't expect them to do it for free, or the same
price they plug for. Some tire places around here will plug a tire free,
even if you don't buy all your tires there. It's good business, I think.

Plugging is illegal (at least in IL) and they must use a plug patch combo.
It's a single device (resembles a weird mushroom). PUll it through from the
inside and the patch portion and plug work as one unit.
Larry

It depends....

If you have z rated tires or are likely to do hi speed driving then you
should have what's know as a patch n plug installed which is a combination
of plug and patch as the name implies.  If your car is your basic grocery
getter and used primarily in commuting without sustained high speed driving
then a plug is fine as long as the hole isn't too big and the guy knows what
he's doing who is installing the plug.  Most dealerships that I deal with
are shying away from the plugs due to liability issues and because so many
newer cars are equipped with higher speed rated tires and nobody can foresee
what a driver will subject the tires to.  I personally plug my own tires and
have never had a problem, just be sure not to try to repair a hole on the
sidewall or of the tire has deformed or now rides rough or with any sort of
imbalance as this may indicate slipped belts or other internal damage.