From a physics standpoint, it's essentially irrelevant what mechanism is used to deliver some matter – whether by rocket or by particle stream, you'll still have to accelerate all that matter to the necessary escape velocity, and heaving all that mass out of Earth's gravity well still requires the same amount of physical work.
Rockets have one big disadvantage – they're subject to the rocket equation. They do not only have to lift the payload, but also the rocket engine and all fuel, and all fuel to lift that fuel, which is wildly inefficient. Of course, there are ways to improve on that.
Launch the payload with an engine but without an energy source. The energy required for propulsion is provided externally, e.g. via solar panels or a ground-based laser. Reaction mass will still have to be taken along, which is subject to the rocket equation.
Use laser propulsion, where light itself transfers impulse onto the payload.
Perform all acceleration up front with a stationary device (e.g. a railgun) so that the payload requires neither engines nor fuel. Due to the high accelerations, this tends to be unsuitable for delivering life forms alive, but for raw materials this poses no problem. This would be the most realistic option for cheaply delivering large quantities of low-priority cargo on an interplanetary scale. If you want to launch from Earth directly to the target planet, the friction caused by the atmosphere is a major problem (you do not want your cargo to burn up).
Depending on a lot of variables (mostly, scale), the most economical solution would be either to use cheap rockets to lift cargo to an orbital railgun, providing initial delta-v to a small rocket via a mass driver, or building a ginormous vacuum tube up into the higher atmosphere through which cargo is accelerated. See for example the Star Tram concept as an interesting example, and the Surface to Orbit page on Project Rho for comparisons of various ground launch concepts.
Accelerating large units (a couple of tons) from a stationary device is logistically easier than accelerating small units (microscopic dust or single molecules, i.e. a gas or a plasma). The latter requires additional energy to break down the materials in the first place, and a lot of effort to slow down, capture, and recombine the transferred matter.
: The technical term is “exponential”