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If the sidekick kills a same (new) lvl minion solo (i.e. one lvl below me) then he will get the exact same exp as he would if he was not sidekicked and killed a same lvl minion.
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...which is less than what he would have gotten for killing that same minion while not sidekicked. A level 25 hero taking down a level 25 minion gets more XP than a level 20 hero taking down a level 20 minion - and a level 20 hero defeating a level 25 minion gets substantially more than either of them.
I don't know what it did to the rest of the team's XP (if anything), but I do know that the second time I ran Sister Psyche's TF, I was sidekicked in the first mission, because I was 23 and didn't like the look of the 26s that greeted us. The second mission started with 25s, so I dropped the sk. Before long, we were back to 26s and I was getting more XP for them not sked than I had gotten in the first mission while sked (and nobody had dropped out of the team), so that looks pretty clear to me that being a sidekick reduces the XP you get for any given foe.