First I was trying to use Toad for MySQL. Although it is very powerful program it didn't have good way to back up whole DB the way phpMyAdmin does.
HeidiSQL creates backup very similar to phpMyAdmin with some small differences, so I hope there could be a way to get exact results.
One is these setting that are added to the backup file by phpMyAdmin:
SET SQL_MODE = "NO_AUTO_VALUE_ON_ZERO";
SET time_zone = "+00:00";
Dump TIMESTAMP columns in UTC (enables TIMESTAMP columns to be dumped and reloaded between servers in different time zones)
Also I'm not sure if HeidiSQL is using these settings:
Enclose table and column names with backquotes (Protects column and table names formed with special characters or keywords)
CREATE TABLE options: AUTO_INCREMENT
Dump binary columns in hexadecimal notation (for example, "abc" becomes 0x616263)
These are default settings that most webhosting companies are using:
https://cloudup.com/cvSUDZX-yxi
Here you can see comparison of one exported table:
https://cloudup.com/c7L54ZV1NVt
Thank you!