D&D doesn't care about how much you succeed by, it is a totally binary resolution system.
He means that a bonus enables you to effectively roll above 20, whreas a reroll does not. Therefore (ignoring other modifiers) with a +2 bonus you can achieve a DC 22 task, but with a reroll you can still only achieve a DC 20 task.
Additionally, with the contest rules, it's not a binary resolution system. Opposed rolls care about your compared totals, not just a binary success/failure.
I totally agree with you that having both is just too fiddly for words. Some things giving +2 and others giving advantage is a mess. Of the two, I prefer advantage because I find it a pain tracking itty-bitty fiddly modifiers.
I wish there was a Higher Ground advantage. I'll probably houserule that. I always loved the idea of characters jockeying for position and maneuvering to get advantageous positions, and higher ground should be a big part of that. In the past its given a +1 bonus or so, which has never been enough that anybody cared; but advantage would open up more tactical movement.
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