The cross browser issues are more to do with a lack of skill than anything in the technology. You can develop cross browser layouts with either a table based or css layout perfectly fine. The main reason people usually argue in favor of the table based layout is a lack of skill doing the same thing with css. I've yet to see anyone offer any other reason. All the usual arguments against css could be easily solved by learning css a little better.
I've been developing css sites for years and there have always been ways to deal with the cross browser issues. Today those issues really break down to a few tweaks for Internet Explorer since most every other browser in existence adheres pretty well to the standards. My current process is to develop a site in Firefox (currently my preferred browser) and periodically test the site in other browsers. At the end I generally have about a half dozen lines of css at most that need to be tweaked for IE, which I'll include in an IE specific stylesheet. I'll use a conditional comment to show that stylesheet to IE only and can even easily control which version of IE sees it.
All told it adds about 5 minutes of development time and is quite easy to achieve. It's much easier to do than it is to explain.
Something most people don't know about tables. In order for a browser to display a table it needs to read the code twice. Before it can begin to display a table cell the browser needs to first understand how many columns and rows the table has. So it reads the code once to understand the basic structure and then a second time to display the table. If you've ever been to a site that shows as mostly empty and then suddenly the whole site appears it's generally because of the wait time while browsers are making that first pass at the table code.
As you start nesting tables inside other tables it becomes more complcated for the browser and so the wait time becomes longer.
Here's an old article about ESPN switching from tables to css in a redesign. It's from 2003. Among other things here is the savings in bandwidth as reported in in the article.
Projected bandwidth savings:
* 2 terabytes/day
* 61 terabytes/month
* 730 terabytes/year
One more thing to add to the discussion. Usually if you want to know the best way to do something you consult an expert in that something. If you want to know how to build a rocket you ask a NASA engineer and not the owner of the local grocery. Go out and find the people who are the thought leaders in web design and development. Find even one that recommends using tables to layout your site. I'll save you time. You won't find any, because there are no good reasons to layout a site with tables other than not understanding how to layout a site with css.