Neither. I believe the fossil record, as far as it goes. I don't believe one can make honest taxonomic definitions from a single thighbone fragment or jaw or whatever; all too much of the fossil record is so fragmentary that it really should have been classified as "curious".
But, there are a number of interesting fossils that get just as quickly downplayed by the evolutionists as archeopteryx by the creationists. Things like fossilized dinosaur footprints crossed by very human looking footprints in the same strata.
As for strata dating, I believe in at least one major flood and probably 3. strata from prior to these events is misdated very easily, as they each laid up a sudden accumulation. The clean limestone regolith (here in Illinois, ranging from surface to 200 m down, depending on where you are) is most probably, as near as I can tell, the result of the noachide flood. Everything since then was laid up by the after effects of that flood and the ~4000 years since. All of the river valleys I have seen - throughout the world - have been quite obviously both young and formed by a vastly greater water flow than currently supported. As an example, the Illinois river has cut about 3m down from the "flood plain" - which is cut about 10x the width of the river into the surrounding landscape.
Now, I'm no fool - I know about carbon dating and ice cores and tree cores. tree cores were used to date - from the current trees to the petrified specimens - to reach to about 5000 years before present. I think that if the creation of C-14 in the upper atmosphere was changed for some reason, that would badly skew C-14 dating. I read a very interesting piece recently about the varying ages of carbon in samples.
At best, I think, we have made a number of assumptions in many aspects, and the people in one field rarely understand the assumptions being made in a related field. We look at the deposition rates in modern situations, and assume deposition rates will be similar throughout the time-span.
I most emphatically do not believe the earth was made from nothing in 6 days 6000 years ago or so; I do not believe that the earth was uninhabited by any life prior to 6000 years ago; and I do not believe the multitude of life forms on the planet were made from nothing.
And um, no, not a satanic atheist conspiracy, but a greedy man. and then perpetuated because people have reputations at stake or a need to believe. To a man who is greedy and self-centered at his core, or who has a cause to hate a church, there is ample reason to believe in something that lets you discount Gods.
Incidents of soft-tissue fossilization - and feathers easily qualify as soft tissue - are extremely rare. People are claiming that in archeopteryx, there has been 80% soft-tissue fossilization! I'm just amazed! Where are our fossilized parrots, cormorants, sparrows and such with feathers? What's that? Oh, there aren't fossils of modern things. Tell that to the fish they found in Africa, living peacefully, while it's relative - same morphostructure - "30 million" years old - was fossilized. we find fossils that were obviously horses, or Mastodons, which easily lasted until the human era. There should be fossilized birds with fossilized feathers. There might be, I'm no archaeologist. But I don't want to hear about crazy mixed things like rehona.
Visuals unlimited has (1) fossil feather impression, and Archeopteryx. the fossil feather is not in combination with a skeleton.
Frankly, I find the Archeopteryx "feathers" over-done - like someone wanting desperately to prove something. But it not to me impossible that that someone was not human; I believe in supra-human agents. Such might seem impossible to you. Our razors shave at different places, it seems.