If the "problems" you speak about are the weak performance of previous AMD processors, they are gone now. The K6 line and below had pretty weak FPUs compared to their intel counterparts, but this was partially alleviated by their original 3DNow! SIMD instruction set for floating point math. Ever since the Athlon classic however, AMD processors have significantly better FPUs than their intel counterparts, or any other x86 processor for that batter, including the recently released intel P4. However, intel has a more widely accepted SSE(and recently SSE2) SIMD instruction set, even though AMD has been pushing 3DNow! longer than intel has. With optimized code, programs will run faster with SIMD instruction sets than the traditional x86 FPU. That enables P3s and P4s to keep up, and often outpace comparable Athlon Tbirds.
However, the difference in most applications isn't that large, and for the most part performance is about the same, with AMD in the lead in most applications. Given the lower price and higher clockspeed/availability of the Athlons(unless you're talking about P4s), AMD processors are the obvious choice for a new system.