Is there any efficient easy way to compare two lists with the same length with Mathematica?

Question

Given two lists A={a1,a2,a3,...an} and B={b1,b2,b3,...bn}, I would say A>=B if and only if all ai>=bi.

There is

Answer 1

Comparison functions like Greater, GreaterEqual, Equal, Less, LessEqual can be made to apply to lists in a number of ways (they are all variations of the approach in your question).

With two lists:

 a={a1,a2,a3};
 b={b1,b2,b3};

and two instances with numeric entries

na={2,3,4}; nb={1,3,2}; 

you can use

And@@NonNegative[na-nb]

With lists with symoblic entries

And@@NonNegative[na-nb]

gives

NonNegative[a1 - b1] && NonNegative[a2 - b2] && NonNegative[a3 - b3]

For general comparisons, one can create a general comparison function like

listCompare[comp_ (_Greater | _GreaterEqual | _Equal | _Less | _LessEqual), 
         list1_List, list2_List] := And @@ MapThread[comp, {list1, list2}]

Using as

listCompare[GreaterEqual,na,nb]

gives True. With symbolic entries

listCompare[GreaterEqual,a,b]

gives the logially equivalent expression a1 <= b1 && a2 <= b2 && a3 <= b3.