<p>We are all talking about the efficiency of the algorithms and it depends on input size -basically.</p>

<p>How about the system specifications of current computer that runs the algorithm? does it make any difference to run a different sorting algorithm in a Core 2 Duo 2.6 GHZ, 4 GB RAM-computer or in a P-2, 256 MB RAM-computer?</p>

<p>I am sure that there must be a performance difference. But, I want to know what is the real relationship between algorithms and system specifications...</p>

An increase in hardware performance will give you a constant C times the running time of your algorithm.   Meaning if you have computer A which is overall 2 times slower than computer B.  Than your algorithm will be twice as fast on computer B.   Twice as fast though really makes hardly no difference when you consider big input values to an algorithm though.
In big O notation
that is to say you will have something like O(n) compared to C
O(n) = O(c
n) = O(n).  The complexity of the algorithm and general running time for large values will be about the same on both Computer A and Computer B.
If you analyze an algorithm's running time using something like big O notation, then you will have a much better idea about how the algorithm really works.   Computer performance won't give you any kind of advantage when you are comparing an algorithm that is O(logn) compared to O(n^2).
Take a look at some of the data values for n:
I will assume 1 second per operation for the slow computer, and 2 operations for second for the fast computer.  I will compare the better algorithm with the slow computer with the worse algorithm with the fast computer.
for n = 10:
Algorithm 1: O(logn): 4 operations 
  Slow computer: 4 seconds
Algorithm 2: O(n^2): 100 operations 
  Fast computer: 50 seconds
for n = 100:
Algorithm 1: O(logn): 7 operations 
  Slow computer: 7 seconds
Algorithm 2: O(n^2): 10,000
  operations  Fast computer: 1.4 hours
Large difference
for n = 1,000:
Algorithm 1: O(logn): 10 operations 
  Slow computer: 10 seconds
Algorithm 2: O(n^2): 1,000,000
  operations  Fast computer: 5.8 days
Huge difference
As n increases, the difference gets bigger and bigger.
Now if you tried to run each of these algorithms on a faster/slower computer for a large input size.  It wouldn't matter.  Hands down the O(logn) would be faster.