The Buran looks similar to the US Shuttle, but is significantly different. I wish I had noticed this thread earlier, this is one of my areas of knowledge.
The US shuttle has three massive SSMEs, and the airframe is built very differently than the Buran as a result, which relies on the Energia booster to get it all the way to orbit. Buran was rated to carry a little more payload, but it was essentially payload itself.
The Buran was more sophisticated than the US Shuttle, understandable considering that it first flew almost a decade afterwards. Unlike the US shuttle, it could fly a mission profile completely automatically, from takeoff to touchdown without human intervention. This was demonstrated on its first and only launch when it took off, orbited, and then landed (in a 30knot gusting crosswind) all on autopilot. The story is that the US shuttle probably has the same capability except for an astronaut driven requirement that the gear can only be deployed manually, but I don't have a good reference for that other than the conjecture in Jenkin's Shuttle.
Long story short, the Buran was an aerodynamic copy of the Shuttle to save time and development expenses (hence the appearance), but the similarities are skin deep. Both have advantages and disadvantages, and that pesky collapse of the soviet union means we'll never know how the two fare against each other in real performance.