I see nothing but problems for Christians in these geneologies. If they're both for Joseph then they have no bearing on Jesus because he wasn't Jesus's father. If Matthew's is for Mary then Jesus gets disqualified from being Messiah since he would be a descendant of Jeconiah. If Luke's is for Mary we have the same problem. Luke doesn't mention Jeconiah, but he does mention his son and grandson. Mary would still be a descendant of Jeconiah. Either way Jesus is SOL.

The reality is probably something more like this. Mark has no geneology because it was composed before the destruction of the Temple, where geneological records were housed. Anyone interested in Jesus's lineage could check out the records in the Temple. However, Matthew and Luke were composed after the destruction of the Temple so there were no geneological records left. So they made shit up. They probably only had a passing familiarity with "the Bible" so they took some geneologies from the OT and then added stuff to them. Matthew probably didn't know anything about Jeconiah's curse so has no problem mentioning him (since Jeconiah was the last King of Judah). Luke knew his audience wouldn't know anything so he hushed it up by not mentioning Jeconiah by name. John, also written well after the destruction of the Temple, avoids the problem completely by having God say that Jesus was His son. What better pedigree than that?
If God wanted us to be Atheists we'd be born that way.