My toilet seems to be a little, well, underpowered when it comes to flushing. It often "chokes" and "coughs" when flushing only liquid, which seems to indicate that the water pressure isn't high enough for the toilet. When flushing more solid waste, it clogs at least once a week. Can I increase the pressure when flushing to prevent this from happening?
To answer the question you asked, yes, you can get a new toilet that flushes faster. They have a flush strength label on the box, and the faster flushes are done by making the opening between the tank and base larger.
However, a slow drain may be more related to an improper vent or a drain line that's too small or improperly sloped. Without a proper vent, the flow down the drain is held back by the vacuum created by the trap built into the toilet. If the drain is too small, well, large things in a small drain take more effort. And if it's not properly sloped, we all know the direction this stuff flows, and it's not uphill.
To determine if the problem is with your toilet or with the drain, try pouring water into the toilet directly with a bucket and see if it drains fast enough. If that's better, replace the toilet. But if it's still not good enough, you've got some work to do.