I think the main issue with creationists regardless of them being old or young earth is that eventually their "theory" falls apart. I do however think that old earth creationist are seen as being more realistic than young earth are.
To me, when having spoken to old earth creationists, it seems that they are simply twisting the texts into sort of fitting with science and as long as you don't ask to many questions its all fine.
But looking at some of the points they use to explain why an old earth is perfectly explainable and fits with the bible (If that is the one we are talking about) it quickly seem to cause a lot of problems.
1. Days in the bible is argued to mean a long period of time, which explain why the Earth can be billions of years old. Which obviously makes you wonder why in the creation story it says this:
Genesis 1
13 And there was evening, and there was morning—the third day.
This is typically what we humans understand by a daily cycle and not something that refer to millions or billions of years. Its pretty difficult to get a good explanation for that.
2. If God is timeless, omniscient, omnipotent. Why would he need billions of years anyway, 6 days should be more than enough, that makes little sense.
3. On the 7 day God is resting, so how many million of years is he doing that. Remember humans have already been created earlier, so how exactly does that fit with our current understanding of human evolution. Homo sapiens are not million or billions of years old. So how does these creation days convert into years? Do one assume that they are of equal length or do they just change length depending on what seems to fit the best?
So in the end, when all comes down to it, the old Earth creationists ain't much better off than the young ones. The best explanation, I have heard is that this is just a poetic description of the creation.
Which eventually lead to a question about Luke 3 23-37:
23 Now Jesus himself was about thirty years old when he began his ministry. He was the son, so it was thought, of Joseph,
the son of Heli, 24 the son of Matthat,
the son of Levi, the son of Melki,
the son of Jannai, the son of Joseph,
25 the son of Mattathias, the son of Amos,
the son of Nahum, the son of Esli,
the son of Naggai, 26 the son of Maath,
the son of Mattathias, the son of Semein,
the son of Josek, the son of Joda,
27 the son of Joanan, the son of Rhesa,
the son of Zerubbabel, the son of Shealtiel,
the son of Neri, 28 the son of Melki,
the son of Addi, the son of Cosam,
the son of Elmadam, the son of Er,
29 the son of Joshua, the son of Eliezer,
the son of Jorim, the son of Matthat,
the son of Levi, 30 the son of Simeon,
the son of Judah, the son of Joseph,
the son of Jonam, the son of Eliakim,
31 the son of Melea, the son of Menna,
the son of Mattatha, the son of Nathan,
the son of David, 32 the son of Jesse,
the son of Obed, the son of Boaz,
the son of Salmon,[d] the son of Nahshon,
33 the son of Amminadab, the son of Ram,[e]
the son of Hezron, the son of Perez,
the son of Judah, 34 the son of Jacob,
the son of Isaac, the son of Abraham,
the son of Terah, the son of Nahor,
35 the son of Serug, the son of Reu,
the son of Peleg, the son of Eber,
the son of Shelah, 36 the son of Cainan,
the son of Arphaxad, the son of Shem,
the son of Noah, the son of Lamech,
37 the son of Methuselah, the son of Enoch,
the son of Jared, the son of Mahalalel,
the son of Kenan, 38 the son of Enosh,
the son of Seth, the son of Adam,
the son of God.
At which point are we no longer talking about a real person? where in this list does the change occur, if at all? So if the creation story is just a poetic description, then we can assume that Adam probably never lived, which obviously give problems for the bible... and is it realistic to assume that the early Christians thought this as well? Nothing in the bible give the impression that it were the case.
So again, as long as one does not ask to many questions it all fits well together for the old Earth creationist