I don't think that there are any substantive contradictions in the Bible. I think there are different viewpoints of certain events and also what best can be described as "typos", unimportant errors that do not change the message or content of the Bible at all.
I'm sure some one will come up with an ingenious explanation to show that these verses are in perfect harmony.
OK, I'll bite! :D But I don't know how ingenious this is, because it seems all rather straightforward to me:
God uses Satan as a tool just as easily as He used Judas. After all, did He not use Satan to test Job? God is the ultimate inciter of David, but He used Satan to test David in this. The message in both accounts is unchanged though, David had angered God, and I'm really not sure in what way, and God tested David by using Satan to incite David to do a census. Joab was a voice of conscience providing that way of escape the 2 Corinthians 10:13 talks about, but David nonetheless sinned against the Lord.
I always make it a point to view the Bible as fully inerrant because it spurs me onward to deeper understanding of Scripture. I have learned a great deal, and uncovered many wonderful gems in the Word all while reconciling "contradictions". Sometimes I think God allowed these things in the Scriptures just to see if we trust Him enough to believe that He is able to keep His message to us intact.