While sparring is it better to slide to the right or left?

IMO jabbing with elbow dows is more difficult to spot but a jab with elbow outside increases the power, what is more reconmended?

The easy (an most correct) answer is that it depends on the situation that presents itself.

As a rule, I try to slip to the outside of the jabbing hand of my opponant, and circle that way as well. This keeps you moving away from the power side of his cross and other weapons. Granted, it's an ideal situation, and that isn't always the case. Also, there are plenty of good combinations going inside, however, I still try to work outside of his jab.

The angle of the elbow really depends on you and what you are more comfortable delevering. Mine usually come out ot about a 45 degree angle, thus splitting the diffrence. To wide and you cant recover to protect well, too tight and you can get jammed up in your protective posture too easily. But, the angle will vary on what defense he presents that you need to jab around. Don't be afraid to vary the angle, just to make it harder for him to read your incoming attacks.

I'd suggest that a more effective focus is to work target / distance based rather than technique based. That is, if you are in opposites (classic boxer's approach), then certain targets will be in range. Technique selection is based upon hitting the available targets not I want to use an elbow, now I have to do something so I can use an elbow (or any other technique for that matter). Target based approaches allow you to more easily stay in the flow and make correct attack decisions much more quickly, imo. If an elbow is the correct choice, given target and distance, then power generation, distraction / covering, etc tend to take care of themselves as part of delivery.

Joe Lewis (the karate guy not the boxer guy ) used to say it this way "Kata is where you show the perfection of your technique. In fighting the objective is to hit that sucker. Whether your fist is at exactly the right angle doesn't really matter."

My two cents.

I'd say Lewis is right on the mark there.