How should we play?.
Every musician needs both, some play with more feeling, some others with more technique. Is up to you. Personally I like 60% technique/40% feeling.
The important thing here is you NEED BOTH. Why?. Well if you have attitude but you randomly strum your strings you'll make noise.
Now you go full technique you become a robot, is boring just like hearing a complex MIDI, never go full technique.
So you have to find your "mix", that is a slow process of self discovery.
Now by feeling I don't mean that you have to be the instrument, hump the instrument, kiss the instrument, NO, nothing weird here. You have to play what you feel and transmit that on your music, you don't have to play something because theory say so. Music theory is a tool, a guide, but you decide how to use it.
Listen some blues/jazz bands they know how to express themselves. Listen some metal for pure energy(that's why we headbang so hard), etc.
Adding technique to your music.
Learn vibrato, bending, tapping, sweep picking, extreme downpicking, pinch harmonic, etc. Once you know how to properly execute them, use them regularly, don't be shy. These techniques break the monotony and make your song more interesting.
Adding feeling to your music.
Rule #1: You have to be in the mood to play, don't force yourself.
Are you excited? Let it flow and make it loud.
Are you sad? Let it flow too, let me hear that sad melody.
Everything works, every emotion adds something different.
Now mix both.
Mix your feelings with your techniques and you'll get your music signature.
For example a sad bending, sounds like a long and slow bending, very powerful.
Remember "EVERY MUSICIAN NEEDS BOTH FEELING AND TECHNIQUE"