Balancing Playability vs. Performance
We already know that setup can affect tone and playability, often in an inverse relationship. This is further extended in a live setting towards performance. Often tone can be compromised slightly in a live setting without much notice from an audience, at least relative to a recording. The audience's perception of your performance, however, is not simply about how well you play guitar, but how you look doing it.
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Strap Length
The most obvious adjustment when moving from rehearsal to performance is strap length. The lower you sling your guitar, generally the harder it is to play. Or the more adjustments that need to be made to your playing. Slinging your axe low is often seen as cool and can enhance your stage image. It's good to try to embellish your image, but of course that needs to be balanced against your actual playing.
You should rehearse standing up as you would at a gig. If you are sitting down, the guitar is in a far more comfortable position than standing up. As mentioned in Holding the Guitar and Pick, you should sling your guitar on your picking hand hip/side, with the headstock extending further away from your opposite hip so that your fretting hand reaches out to it. This reduces the strain on your fretting hand wrist.
If you sling lower, there are often a few adjustments to be made. First, you may need to point the neck more upwards towards the sky than usual to alleviate the fretting hand. The lower the neck is relative to your elbow, the more extreme angle your wrist has to make to fret. Second, the angle your picking hand wrist makes will be more perpendicular relative to the strings than otherwise. This may mean you have to adjust your wrist, but this is likely going to feel limiting and unnatural. More likely you will have to get a feel for the more extreme angle that the pick hits the strings. It can make palm mutes especially difficult, as the part of your palm used to mute any particular string will be closer to your pinky knuckle than your wrist.
Keeping the above points in mind, you should find a comfortable spot to sling your guitar, so that you retain virtually all your playability. The most important thing is to rehearse that way. As you become more and more comfortable playing standing up, you will find you can lower the strap while minimizing impact to playability. My advice is to start with the guitar slung high, so it is basically just slightly more difficult than sitting. Once completely comfortable, move it down, but just a little. Over a few weeks or months, you'll be able to sling it to a point where it looks quite nonchalant without having lost any playability.
Solo'ing
Solo'ing can be particularly difficult standing up with a low slung guitar. A simple trick to alleviate this is to put your left foot on top a stage monitor or something similar, then resting the guitar on your left thigh. This resembles sitting using classical position, with easy access to the higher frets. Usually when you are solo'ing, the audience wants to see your playing more than body movements and axe swings.
Body Movement
When you go to a show, the last thing you want to see is a guy standing perfectly still. Even if he's playing extremely technical music note-perfect, it just seems boring and soulless. Adding some body movement can make all the difference to a performance.
The simplest thing to try is to move your head and/or body in time with the rhythm, with the extreme example being full-on headbanging. Other things to try are jumping so that you land on the downbeat for a chorus or otherwise powerful section. Or axe swings where you hold the neck of the guitar up high with the fretting hand and slam it down back to normal position on the beat - this can be further enhanced by raising the guitar using the right hand. (Dragonforce was the most extreme example I've seen of this, with both guitarists finishing solos by doing 360 spin jump axe swings off of raised platforms.) There's also the mellow version of the axe swing that looks more like a rocking motion, leaning back and forth, so that the guitar is pointed upwards on beats 1 and 2 and held downwards for beats 3 and 4 - totally 80's but still appreciated. Or just jolt the guitar with your fretting hand when hitting an accent.
The most important thing is to look like the music is emotionally influencing you. If you don't look spirited, the audience won't be spirited by your performance. Even if they are for some other reason, they will not connect with you and would feel little regret if you were substituted with a backing track.
Facial Expression
When I focus exclusively on playing guitar, my face makes some weird, off-putting expressions. I suck my lips into my mouth, squint my eyes, and make some confused looking eyebrow motions. I also focus my eyes exclusively on the fretboard. These are all distracting for a live performance. Making eye contact with the audience, yelling at them, and otherwise making expressions that follow the accents and mood of the music make the audience feel involved and inspired.
Stage Tricks
You can also resort to stage tricks to increase your performance. Things like spinning the guitar completely around your body, playing it with your teeth, or playing it behind your head can impress a crowd, even if they add absolutely nothing to (or actually hurt) the musical performance.
Stage Show
Unique costumes/wardrobe, lighting, stage design, and interaction between band members can enhance a performance. If extreme, however, this can affect your musical performance negatively. Again, it's important to rehearse under similar conditions, ensuring there are no problems.
Know your Audience
Few people are going to a punk show to watch the intricate playing style of the guitarist. Similarly, few people are going to an instrumental rock guitar concert because "He just goes absolutely nuts on stage." Depending on the style of music you play and the audience you draw, you may connect better through excellent musicianship vs. an energized performance.