Both energy and momentum are conserved, but the kind of energy that is in plain view - kinetic energy - isn't conserved. It can convert to potential energy, which is nearly as obvious - as this pendulum oscillates, you can see kinetic energy convert to potential energy and then be converted back to kinetic energy, while slowly both forms of energy are converted into a disordered form. In this case the disordered form is the motion of the air disturbed by the pendulum's motion, and the heating of the thread and the pendulum bob as well.
Momentum and angular momentum are different - for one thing, they are vector quantities, with a magnitude and a direction, so there's no "disordered" form to disguise them. There's also no "potential" form of momentum. Angular momentum and linear momentum are always conserved - even though (as we shall see) that isn't always apparent in day-to-day life.