From the moment that using a computer for audio recording became possible, there has been an ongoing debate regarding the merits and pitfalls of the two systems. One of the drawbacks of using a computer is the cost of all the peripheral equipment you need in order to record, which can include external pre-amps, D/A (digital to analogue) converters, a good quality soundcard and a control surface. Computers are also designed to be used for many different tasks, such as internet browsing, word-processing and gaming, and if they are not set up properly to deal with audio, any number of problems can arise. A multitracker however has all the key peripherals built-in and is designed purely for audio recording, so you can be sure that all the power of the CPU is working on the job in hand, and you wont run into conflicts with any other software!
In the end it really comes down to personal taste the computer is more powerful, and a basic system can work out cheaper if you are prepared to share the use of an existing machine with other applications, but the portable multitracker is the clear winner when it comes to immediacy and reliability.