Technically there is a difference between more accurate and safe.
A dive computer is a tool to calculate bottom time just like the tables. It is a more accurate device and as the previous post point out you get calculations for actual levels in a multilevel dive. If you start your dive at 50 feet, then go to 60 ft, then 30 ft, back down to 50 ft, then end your dive and surface the computer takes into account the different levels and the actual time you spent at each depth. It allows for more bottom time with a greater degree of safety than the charts alone. The same previous dive the entire calculation would have been 60 ft only for the whole dive.
Certain brands of computers have a reputation being more conservative than others, while some allow you to choose more conservative profiles over more liberal profiles. If you wanted increased safety then choose a more conservative computer.
Personally I trust my computer to do the calculations for me since I'm not very good at math. There is also user error involved in using the tables, and I feel like I'm more likely to misread and miscalculate the dive. I know essentially how to use them and what they represent. It's just that I'm likely to mistake my pressure group and time calculations. In this case I find the use of a computer safer for me personally.
Technology is a wonderful thing. When I was buying new golf clubs recently the salesperson said, "why not take advantage of the new technology to hit the ball straighter and farther?" Same is true for diving. The computers make diving easier. Not necessarily safer than tables, just easier to use than tables. It is up to you to dive safer by using the computer appropriately and actually monitoring it routinely during a dive. It doesn't do you any good if you don't check it, and then realize that it put you in Deco because you weren't paying attention to your time and your depth.