I am replacing an electrical outlet, the wiring connecting to the outlet is in poor condition. I am going to cut the wiring back to where the wires are not damaged. To connect the outlet I will need to pigtail some wire to extend the length (this is in the box not behind the wall).

The outlet has 2 black wires to the two dark terminals and two white wire to the silver terminals and a ground.

I am getting confused on a few articles that I am reading. Some indicate that it is best to pigtail the blacks for one connection to the outlet (same for white). Since I have to do pigtails anyway, I can wire it that way. Of course, there are some contradictions.

Is one way better than the other?

You may add a length of wire as long as the connection is made inside the box. You may connect the two blacks and add one pig tail, them connect the two whites and add a pig tail. Or you may add a pig tail to each wire. Your choice as long as the connections are made inside the box.
I would probably go with connecting the two wires and adding one pig tail, fewer connections and takes up less room in the box. However, that is probably more difficult to do than just adding a pig tail to each wire.

It sounds like your receptacle was used to "junction" the circuit... two wires in and two wires out. Pigtails are the best way to go as they insure that the wiring does not have to go through any receptacle. How is the receptacle grounded?

Use Term-Nuts from Ideal. I won't go into details because I lost what I typed. One of the other reasons I'm not here any more. Making the grounds work is harder, but it depends on what you have to work with. You have to ground the outlet and the metal box with a wire. Your not allowed to relay on the screw except in special circumstances.

It is "grounded" an old fashioned way that is no longer acceptable.

Sorry, I had trouble figuring out the reply here and kept losing paragraphs.

I did do the pigtails and the receptacle is grounded but I understand that does not address the box issue. For now, I am leaving the circuit off and will only put it on for specific purposes if needed.

The side of the metal box is rusted, that is why the wires were in bad shape (the leak that caused it has been repaired). I have it on the list to open up the wall area-get a new box.

When conditions are good, I can do simple mimic stuff. Other than a BAD experience with an electrician on this past Friday, I don't have a problem getting help. I just need to do it in stages and I want to understand even if it is not something I would do myself.

If you plan on replacing the box you can get what they call an "old work box", which generally is a little larger and deeper than your existing metal box. I don't endorse dealers normally, but Lowe's has an old work box with 2 wood screws mounted on an angle inside the box that you can screw to a stud.(I think Allied makes them too if you can find them elsewhere). The screws hold the box solid and allow for adjusting the box to be flush with the finished surface. If the current box is not next to a stud, then there are alternative "old work boxes" that work fine also. A new deeper box will allow you to make your connections and probably stay within code for the box size. If you are comfortable making the connections, then two blacks and black pigtail under one wire nut and two whites and white pigtail under another wire nut. The pigtails go to the appropriate terminals on the outlet.

To replace an old metal box.

Carefully pry the box away from the stud slightly. You should be able to separate the box and the stud by 1/8" without damaging the drywall. Then cut the nails between the box and the stud with a sawsall (reciprocating saw) and metal cutting blade. Remove box and replace with an "old work" box.

Damage to the drywall should not be necessary.