That is a difficult question to answer because Mac OS X is still in development, which makes it hard to guess what features it will have, and how it will perform.
We can say this -- Mac OS X and the BeOS have different target markets and take two very different approaches to operating system design. Mac OS X is based on a combination of established (aka older) technologies -- Mach as a microkernel, Objective C as a language, Display Postscript as a graphics language. These technologies are then melded into a whole using the OpenStep toolkit.
The BeOS, on the other hand, was designed from the ground up following a concept we call the "Media OS." It's simply not enough to start with an existing OS, add a few features, and call it a media-oriented OS. The engineering team at Be didn't start with an existing OS and transform it, they started with the Media OS concept and optimized every portion of a new OS -- the BeOS -- for handling digital media.
The BeOS is designed to meet the high-performance needs of digital content design and Internet communications, removing the limitations and complexity of the aging architectures of current mainstream operating systems. The BeOS is the first new operating system designed to unlock the door to much more powerful personal computers, and extract more performance from the systems we use today.
The two systems also have very different target markets as their design centers. Mac OS X's design center seems to be for servers and the enterprise business user. The BeOS's design target is interactive media, and the individual who sits down to design digital content. As Apple has stated, it bought Next in order to establish a better solution for Apple in the enterprise market, and converting the Next OS to Mac OS X will help them accomplish that goal.