The way the browsers render table borders does vary considerable. There is no way round this using just html. However, if you implement some CSS on your site then you can have much greater contorl over the way your borders display. For exmple this CSS code might give you an idea of how to alter things;
Code:
<td style="border-top:3px solid #CCCCCC; border-left:3px double #CCCCCC; border-right:3px solid #CCCCCC; border-bottom:0px none #CCCCCC; background-color:#CCCCCC; color:#333333;">
There's allot more you can do with CSS and smarter ways you can implement it. For example, with a little alteration you could apply that CSS to all the td table cells rather than having to define each individually.
Rememeber also to run your site through http://validator.w3.org/ to check for any errors.