This depends on the type of system you have, and what you are trying to do.
The Alpha is a RISC processor: it has fewer and simpler instructions. Thus, at the same clockspeed, it will generally be slower than a CISC processor. But, being simpler, it will be easier to build processors that run at higher speeds. The fastest Alpha (now at 833MHz) will outpace the fastest Intel processor (1 GHz.) This will remain true for many years to come. (It will also be more expensive.)
In BogoMIPS, Alpha's up to the 164 show a speed approximately equal to the
clock frequency in MHz (like Intel's 486 and early Pentium processors.) The
264 has a BM value of twice the clock speed (like Pentium MMX and higher.)
This, however can not be taken as a true indication of the speed for
real applications.
RISC instructions are fewer and simpler, so you need to execute more of them to get the same amount of work done. On top of that, they are also larger. So, to keep your Alpha running at full speed, you need large caches and high memory bandwidth. Most Alpha's have two levels of cache on chip, and the newer boards also provide wide (128 or 256 bit) memory busses. Some of the older Alpha systems, however, do suffer from lack of memory bandwidth.
The Alpha has earned itself a reputation for floating point performance. However, it takes a very good compiler and libraries to achieve the optimum. Until recently, this meant that the real numbercrunchers would often revert to Digital Unix. Recently, though the compilers in the Open Source arena still lag behind, large improvements have been made w.r.t. the libraries and compilers. Compaq has ported the Tru64 (Digital Unix) compilers and math libraries over to Linux. They are available for free download for academic and personal use, commercial use does require purchasing a license.