the trouble is that when I design websites in either resolution, they look slightly out-of-sinc on the other resolution. ust usually the spacing of the words on the page (where they start and end) etc and some table issues.
That can happen, especially for table-based layouts. Table-based layouts should never be done anymore because they are obsolete. If I have to choose which resolution it looks best in, I would go for the 1024x768 because the overwhelming majority have that resolution (or higher). Fortunately, with my site, the only issue with 800x600 it has is that it makes everything look gigantic (logo, text; the design fills the entire screen). It is still 100% readable and usable.