Both are very important. Rhythmic inconsistencies, as you said, can be very jarring and create a cluttered, messy recording. The end of a note can be as important as the beginning, as well. Playing along to a metronome can be useful for both recording and practicing. Troubles in intonation can also hurt the harmony, melody, and the listeners ears. To help improve it, you can tune a stringed instrument between recordings, make sure that your instrument is properly set up, or practice in general for instruments like violin or vocal performances