I like both of them, but if I had to choose one, it would be HC 09.
I played HC 06 a lot on the PS2, and it took me a while to figure things out. I had coaches (yes, plural) quit on me during a season, and I couldn't get the practices right and the team was unprepared. I had a bad first season, a horrendous second season, and an improved (but still bad) third season. After the third season, I believe my contract wasn't extended, but I wasn't outright fired. I started a new coach after that.
My second run was much better as I had figured out how to hire the right assistants and improve their trust with me. As the Browns, Vince Young dropped to me in the draft, and the team's success pretty much hinged on his play. I had the Browns in the playoffs by the 3rd season and won a Super Bowl by the 5th season. Young had become a beast because I had hired the right OC and QB coach to develop him.
I loved the practices and staff meetings, even though that became boring and redundant. I also loved the "range" a player would have in his ratings.
The drawback was the fact I couldn't change the quarter length. It bugged me to see how "good" my defense was ranked only because we played 20 minutes versus the 60 minutes simmed by the other teams. I also discovered the AI would cut young players, who were buried on the depth chart. I scoured the waiver wire and in one season I picked up some rookies: a CB (2nd-round pick), LG (3rd-round pick), and a LE (1st-round pick). It was like gaining extra draft picks without having to trade anything.
So why do I prefer HC 09? I liked the improved AI. I was playing this game without the knowledge of the draft classes, so that did slow my team's progress. I did build up the Panthers to be a really good team in the NFC, but the game got harder as I progressed. Better coaches appear in the game and the game figured out my tendencies. I really had to develop my players and, especially, my playbook.
Now, the knowledge I gained from this forum would put me in a better position, and I would probably have an easier time in the beginning - maybe even winning a couple of Super Bowls.
I found HC 09 to be a bigger challenge in the long run.