(Sound quality will be about the same, though.) Basic indoor antennas start at about $10, though some cost much more. If you're close to a broadcast station and there are minimal obstacles between your antenna and the tower, you should see a clear, continuous picture that might be better than what you get with analog. With any of these scenarios, you should first try a basic indoor set-top antenna designed to pick up both VHF and UHF.
(However, digital stations in some areas may move to the VHF band next February, when analog channels vacate their station frequencies.) The UHF band is more directional than VHF and more sensitive to obstacles (such as trees, tall buildings, and mountains) that lie between your antenna and the broadcast tower. Most analog stations are in the VHF band, channels 2-13, while digital signals are transmitted mainly over the UHF band, 14 and higher. Digital TV offers potentially better picture quality and more channels than analog over-the-air broadcasts, but getting digital signals might not be as easy as plugging a converter box between your antenna and TV.