I love both games and I can offer a different perspective as I am a poker player that has only recently started playing chess.
Poker is a game of skill. Due to the mechanics of the game (most importantly hidden information and randomization), skill is hard to see to the untrained eye.
Much of the skill in poker lies in correctly evaluating the situation. Being able to calculate odds in poker is a very important skill, albeit an elementary one. Odds calculation in poker is about equivalent to knowing which pieces can attack each other in chess. There are many more elements to take into consideration in every poker decision such as: opponent’s range of hands, opponent’s perception of your range of hands, opponent’s tendencies, cards on the board, future cards on the board, and how your actual hand relates to all of that.
Will the better poker player win every hand? Of course not. Will the best player win every tournament? No. This does not mean that poker is not a game of skill, but rather that poker skill is not necessarily realized in a short number of hands.
As far as one game being more of a ‘skill game’ than the other, that is a ludicrous proposition. Apples and oranges.
Poker is an intensely skilled game. Yes, there are random elements. And there is critical information in poker that is not available to all players. But over a long enough series of hand, the random element evens out. Each players gets their share of the good and bad hands. The skill is knowing when and how much to bet. Part of this is psychology, part is a knowledge of mathematics and probability. I can assure you, over time skill wins out. Compared to chess, yes the outcome of a single event is somewhat more influenced by chance. Some one might have a lucky hand, even a lucky night, but day after day in professional games skill carries the day in the long run.
Edit: Is poker "more" skilled? No, its not. It has a different set of skills and knowledge need to play at the highest level. But I wouldn't go telling a professional poker player that he is less skilled that you. If you really think that, I am sure he would be willing to empty your wallet for you.