>Here is a sample:
>
>

>declare @t table (id int identity, col1 Int, col2 Int)
>
>insert into @t (col1, col2) values (1, 3), (2, 5)
>
>select * from @t where not (col1 > 3 and col2 < 6)
>
>select * from @t T where not exists (select * from @t T1 where col1 > 3 and col2 < 6 and T.id = T1.id)
>
>select * from @t where col1 <=3 or col2 >=6

>
>Normally NOT (condition1 and condition2) translates into opposite condition1 OR opposite condition2

Yes, after second verification, I see that the execution is the same.

I always use the NOT in such approach as it is more easy to understand. When I have something like this:

DECLARE @ModDate DateTime
DECLARE @NoStatus Int
DECLARE @ModDate2 DateTime
DECLARE @NoStatus2 Int
DECLARE @ModDate3 DateTime
DECLARE @NoStatus3 Int

SET @ModDate='2013-11-09 10:31:18'
SET @NoStatus=5
SET @ModDate2='2014-11-03 10:31:18'
SET @NoStatus2=8
SET @ModDate3='2014-11-03 10:31:18'
SET @NoStatus3=7

SELECT Client.Numero FROM Client (NOLOCK)
 WHERE NOT (Client.ModDate<@ModDate AND Client.NoStatus=@NoStatus) AND
  NOT (Client.ModDate<@ModDate2 AND Client.NoStatus=@NoStatus2) AND
  NOT (Client.ModDate<@ModDate3 AND Client.NoStatus=@NoStatus3)

...it seems more easy to understand that the second one:

DECLARE @ModDate DateTime
DECLARE @NoStatus Int
DECLARE @ModDate2 DateTime
DECLARE @NoStatus2 Int
DECLARE @ModDate3 DateTime
DECLARE @NoStatus3 Int

SET @ModDate='2013-11-09 10:31:18'
SET @NoStatus=5
SET @ModDate2='2014-11-03 10:31:18'
SET @NoStatus2=8
SET @ModDate3='2014-11-03 10:31:18'
SET @NoStatus3=7

SELECT Client.Numero FROM Client (NOLOCK)
 WHERE (Client.ModDate>=@ModDate OR Client.NoStatus<>@NoStatus) AND
  (Client.ModDate>=@ModDate2 OR Client.NoStatus<>@NoStatus2) AND
  (Client.ModDate>=@ModDate3 OR Client.NoStatus<>@NoStatus3)