If your couch creaks, sways or otherwise betrays some sort of structural damage, you're better off replacing it entirely. No matter how fancy the exterior is, a piece of furniture is only as good as its foundation. Over time, wood weakens and splinters, braces fail and hardware comes loose. In some cases, a professional can take apart your couch and repair the damage, but this can be pricey and is recommended only for valuable antiques or pieces with very high sentimental value.
If you've had your couch for a while or bought it used, there's a chance that the frame is made from solid wood instead of particle board, plywood or MDF. Look underneath the lining on the bottom of the couch to see if the "skeleton" has wood grain. If it does, you have a solid piece that will likely last longer than a new couch made of inferior materials. As long as no structural damage is present, this piece would be a good candidate for reupholstering. A solid wood frame denotes a higher-quality couch, and purchasing a new one at all but the highest price points would be a trade down.
Think about what you hate about your current couch. If it's the color, fabric and pillows, reupholstering can fix all of those things. A good reupholsterer can even stuff new life into saggy cushions and flattened pillows. If the size, shape or general design of the couch isn't quite right, you're better off replacing it entirely. Simply recovering it won't change these factors, and because the difference in price is negligible, you may as well get what you want.
Before you put the old couch out on the curb, shop around a bit to see what's out there in your price range. You may find that many of the moderately priced furniture stores carry variations of the same basic design, and it can be difficult to find something you fall in love with without paying a fortune for a designer piece. Even if you see a few that are OK, they may be slightly too small, too cushy, too ornate or too casual. It's possible that you won't see anything you like better than your existing couch, in which case, reupholstery is a better option. If you simply need a temporary fix until you find a new couch you adore, an inexpensive slipcover is the best option.