I couldn't get to the core of the concept, however gathered sufficient information required to convince myself that operating systems differ based on ISA (eg: x86 and x64) and not on microarchitecture (Intel Pentium and AMD Athlon).
A simple analogy is -
ISA is like C language; 'a standard', to be followed to do something.
whereas microarchitecture is like C compiler; 'an implementation' to enforce those rules or standard.
Excerpt from wiki - Microarchitecture
A given ISA may be implemented with different microarchitectures;
implementations may vary due to different goals of a given design or
due to shifts in technology.
The ISA is roughly the same as the programming model of a processor as
seen by an assembly language programmer or compiler writer. The ISA
includes the execution model, processor registers, address and data
formats among other things. The microarchitecture includes the
constituent parts of the processor and how these interconnect and
interoperate to implement the ISA.
Machines with different microarchitectures may have the same
instruction set architecture, and thus be capable of executing the
same programs. New microarchitectures and/or circuitry solutions,
along with advances in semiconductor manufacturing, are what allows
newer generations of processors to achieve higher performance while
using the same ISA.
The factors which distinguishes different microarchitectures but still implementing the same ISA are-
Execution units are also essential to microarchitecture. Execution
units include arithmetic logic units (ALU), floating point
units (FPU), load/store units, branch prediction, and SIMD. These
units perform the operations or calculations of the processor. The
choice of the number of execution units, their latency and throughput
is a central microarchitectural design task. The size, latency,
throughput and connectivity of memories within the system are also
System-level design decisions such as whether or not to
include peripherals, such as memory controllers, can be considered
part of the microarchitectural design process. This includes decisions
on the performance-level and connectivity of these peripherals.