Power Grid is a game all about, well, power. Each round of the game consists of several phases: An auction phase for power plants, buying resources to power the power plants, a network-building phase to establish your power grid, and the "get paid" phase. The game continues in this order until a player builds to a certain number of cities, which varies according to the number of players.
Power Grid is definitely a step-up from Ticket to Ride and Settlers of Catan. The rules are more complex, so you will need to read and re-read through the rules both before and during the game. The order of each phase in the game is fixed throughout, but within each phase, there are several rules to remember and follow. I recommend making notes in the rule book and consulting this FAQ guide.
What I like about Power Grid is the auctioning of the power plants and the way player order is determined. There can be a great deal of positioning and posturing for who goes where in the turn order. There is a tension that exists as you try to manage both your money and resources, all the way trying to connect cities with the cheapest connection costs possible. The imbalance of both power plants and the map (connections are more expensive in some geographic regions) are offset by the player order and the fact that you can decide where to build and what to buy. I also like the fact there are several expansion maps available. Among my favorites are the Italy and Korea maps.
The downside, as I've somewhat alluded to earlier, is that the rules are a bit complex and "fiddly". Through our first play, we were constantly checking the rules to make sure what the proper procedure was. Some players may be prone to "analysis paralysis" or the tendency to over-think and spend too much time calculating a move. The tension that makes the game fun can also make the game last longer if players get too bogged down.
Overall, I rate Power Grid a 9 out of 10. It is a great game for those who already are in the world of strategy game. For those not, I would point them toward Ticket to Ride or TransAmerica.
Happy gaming! And merry Christmas!