I thought it interesting to look at the different modes of reasoning and how they apply to each game... http://en.wikipedia.org/wiki/Logical_reasoning
Deduction, Induction, Abduction... Among these, I would rate them from most to least complex (or from higher level thinking to lower level thinking) as:
Now, when we play games, we are thinking in essentially two contexts:
Tactics or strategy
I think it's fair to say that basically:
Tactical reasoning = Deduction
Formulating Strategies = Induction and Abduction
A primary difference between human and computer intelligence is that humans find enumerating long lists of deductive conclusions to be mentally tiring. But this is essentially what we are doing when we analyze chess positions through a game tree. It is a simple task, but tedious.
On the other hand, induction and abduction is where human minds really excel past computers (especially induction). I can show a single picture of a dog to a young child, and say "This is a Dalmation", and instantly that child will be able to recognize all future instances of Dalmations he sees. Computers can't do this kind of thing. It is an extremely complex task to categorize information the way people do, but we tend to take this ability for granted.
Chess strength is predominantly dominated by one's ability to reason tactically, to "see things" far in advance. Chess is heavy on tactics and relatively light on strategy. The position evaluation function in chess computer programs is representative of a strategy. The fact that GMs have been able to write out position evaluation functions by hand, resulting in very strong chess programs, kinda proves that there's not *all* that much information contained within a chess strategy... GMs have stumbled upon their strategies through very strong inductive ability. While induction abilities are important to formulate chess strategies, it is *not* as important to play chess and not even to learn chess (I can read a book and use somebody else's strategy; I don't need to formulate my own)... Through the course of the game, chess players are primarily using deductive reasoning, the mode of reasoning that is at the lowest level of complexity/intelligence.
Rote memorization also greatly improves chess strength. A strong player must remember all sorts of openings and variations. Yeah, it's a lot of work for people to do this, but I don't consider memorization tasks to be "complex".
Poker, on the other hand, is almost all strategy and very little in the way of tactics. Can any top poker players write out, by hand, an EV function approximating the value of any position? Absolutely not! There are way too many variables to consider. So, the information contained within a poker strategy is a lot bigger than what's contained within a chess strategy.
In order to play poker well and exploitatively, you must use all modes of reasoning through a game - deduction, induction, and abduction... Yes, poker is light on the tedious and mentally tiring deduction tasks that chess requires, but it is heavy on the more complex forms of reasoning that we have so much difficulty programming computers to do.