"I see your point and I'd use it if I needed to flatter myself. But I'm sticking to the latter. And I'd be sure to mention the starting baseline as well. But I'm sticking to the latter."

Help yourself. Just don't use that type of language in any conversation with anyone else on the planet because you'll likely confuse the hell out of them (take note of the "wtf is this guy talking about" downvotes you've received on this thread)

It's not about flattery. It's about metrics that matter and revenue. Doubling your conversion rate pretty much doubles your revenue. That aside, the goal here is communication. I'd wager that if you said that you doubled your conversion rate, people would grok what it meant (1% to 2% or 5% to 10%-- either way, a big win because it'd double revenue and profit down the funnel). If you said you increased your conversion rate by 10%, I'd wager people would assume that meant something like 10% to 11%.