So, for example, I am doing a song, 'Tere Hawale', Right. I transpose to my comfortable scale, so which would be E Major, right. So I find the chords, and I can have a open + Barre Chord Combination, which is, E Major Open, G#Major(Barre), AMajor, B Major(barre) and so on. Now, E and A Major are open. But the other ones are Barre, they don't have open forms(G# and B). So now I can play like this only, or an octave higher playing the open chords as Barre, meaning E Major as on 4th Fret a D Major Shape (Barre), A major on the 5th fret as a E Major shape, F# Minor as on 5th Fret in a D Minor shape. Now my question is, which of the above-mentioned ways I should play? Or rather when I should play either of the ways, what is the difference? Because Open Chords do not exist for sharp chords, F sharp and G sharp and so on.
That's the beauty of being a guitarist - you have the choice! Yes, it's obvious some of the chords must be played using barres, but the others, such as E and A, could be played either way.
That choice is entirely up to you, the player. It may depend on the strum pattern, as in muting the chords as they're played, giving a sort of syncopated rhythm, in which case, using all barred chords would be the sensible option, allowing that syncopation to be maintained throughout.
The sound of open chords is subtly different from those barred, so your choice is do you want that difference in sound, or not.
There's also the factor of chord movement to consider: if the E and G♯m are played consecutively, you may want to use 4th fret Em barre shape for G♯m, and 4th fret C shape (maybe better than D shape), as there's little movement between the two.
You may, however, have other choices which involve different shapes for the open E and As, which, as a guitarist, you have the luxury of making.
Or, you could capo on, say, fret 4, and play as if in key C, although you say your favourite scale is E, which I assume means you want to use E and A chords whenever you can.
The difference is... well, the difference is what you hear.
How does it sound if you play everything as close to the nut as possible?
How does it sound if you play all the chords as E-shaped - A on 5th fret, B on 7th?
How does it sound if you play it one way in the verse and another in the chorus?
How does it sound if you...
If your skill allows you multiple options, just try them out and choose the best.
(If there's really only one way you can play it, do that. I promise it will be all right.)
You know, your question sounds almost as if you believed that open chords and barré chords are two fundamentally different categories that shouldn't mix in one song. But virtually every song in C major I know contains a C that is generally played as open, an F that is generally played as 1st fret barré, and a G that generally some people prefer to play as open and others as 3rd fret barré. An open chord is nothing but a chord with a "barré" on the 0th fret that you don't need to hold because the guitar already holds it for you.
And every chord (or at least, every triad chord, not sure how this works out for very complex ones) has multiple ways it can be played. Some don't have an open version, but they still have more than one barré version.