All depends on the type of resizer you use. For the most part, you'll just lose luma resolution but actually keep most of the chroma resolution (assuming your camcorder doesn't actually use 4:4:4 and your video format records in 24/30bits per color or 4:4:4). In some rare cases you might see artifacting, but changing the scaler method generally fixes that. If you want slight sharpness increases, use a lanczos or bicubic (sharp) type filter, often people won't be able to tell the difference between 1080p rescaled video using a sharper downsizer and the original video.
You can also expect the video to take up less space and have smoother playback.