A key difference between Biblical Creationists and Old Earth Creationists/Theistic Evolutionists is the emphasis on the doctrine of Sola Scriptura. Sola Scriptura holds that the Bible is the sole and sufficient authority for Christian doctrine (Deuteronomy 4:2; Proverbs 30:5-6; 1 Corinthians 4:6; 2 Timothy 3:16-17; 2 Peter 1:20-21; Revelation 22:18). For the Biblical Creationist, the Bible is held in high regard. Other sources are seen as helpful, but they ultimately belong in the back seat of the car, so to speak. This is why you will frequently see Biblical Creationists referring back to the Scriptures.
By contrast, Old Earth Creationists/Theistic Evolutionists do not refer to the Scriptures as often, and when they do, it's never in the correct context. To give a few examples, they often refer to:
• Secular scientific consensus
• Specific churches/denominations that reject the plain interpretation of Genesis
• Early believers (most commonly Augustine)
• Their Christian friends who hold the same view
None of these sources are authoritative in the Christian faith, yet they are held to be so by old earthers.
Secular scientific consensus is obviously not authoritative in the Christian faith because we do not live in a secular world. Secular scientific consensus is shaky, malleable and often intentionally dishonest. It is shaky because error can be made, even severe errors. As Gregory Dawes noted, "if Newtonian physics needed to be radically revised in the early twentieth century, then we should not assume that even our best theories are established beyond any possibility of doubt." It is malleable because it frequently changes. The Evolution we have today is not the same as it was in Darwin's day. It is often intentionally dishonest because, as Richard Lewontin noted, evidence is often rejected to prevent "a divine foot in the door". The very purpose of Lyell's invention of uniformitarianism was to "free the science from Moses". Appeals to secular science, therefore, do nothing to tell us that Evolution fits the Bible.
Specific churches/denominations are also not authoritative. The authoritative structure of Church doctrine goes from God to the apostles and prophets. Jesus never said "if you had believed Luther, you would believe me, for he wrote of me." He said that about Moses in John 5:46. When Abraham spoke to the rich man, he didn't say "they have the Catholic Church. Let them hear them." He said they have Moses and the prophets (Luke 16:29). And in 2 Peter 3:16, Peter didn't call Paul's writings "denominational opinions", he called them scriptures. Denominations are actually a bad thing, because we are instructed against them (Romans 16:17; 1 Corinthians 1:10). We are told that they are carnal (1 Corinthians 3:3) and lack the Spirit (Jude 1:19).
Early believers, including the Church fathers, are also not authoritative. They are obviously of particular note, but not to the point where they should define our doctrines. Furthermore, the early Church overwhelmingly took the "young" earth position. Compare this to the literal non-existence of any Evolutionary views, even from Augustine. Referring specifically to Augustine, his early view was that rather than taking six 24 hour days, God created all matter in an instant. It is of note that Augustine himself actually seems to have come to his false conclusion based on a faulty understanding of non-authoritative texts. Augustine believed the deuterocanon was also scripture, so when Sirach 18:1 said God made "omnia simul", Augustine interpreted that as "everything at the same time". But the original Greek doesn't say this. More modern translations render it as "the whole world". Effectively, when they cite Augustine, old earthers are using a non-authoritative, erroneous source based on an erroneous translation of a non-authoritative text. What's more is that Augustine eventually repented of this error. In De Genesi ad litteram, Augustine returned to a more plain reading of Genesis. You can also click here to see my previous response to a common misquote of Augustine.
Finally, it shouldn't really need to be said that our Christian friends are not authoritative. As I've pointed out before, there is a huge difference between what Christians do believe and what Christians should believe.
The only authoritative source of Christian doctrine is the Bible. When the Bible speaks of creation, that is what Christians should believe about creation. The fact that Biblical Creationists are content with that, whereas old earthers insist on getting their beliefs from other sources, should tell you a lot about who is getting their views from God, and who isn't.