"TWTR's push to be a digital live video provider is interesting, but we note that bigger competitors such as FB & GOOGL have much stronger digital video propositions for advertisers with much larger and more engaged user bases, deeper granular data for targeting, and proven return on advertiser investment," Thill said.
Twitter has "seen a steady improvement in engagement from its core users, but has yet to translate this into revenue growth," Thill said, noting that advertising revenues in the first half of the year for Twitter are down 6 percent versus the 15 percent gain for the industry.
Twitter year-to-date performance
Thill and his team also cut their price target on Twitter to $16 from $20.
Twitter shares closed 0.4 percent lower at $16.89 Thursday. The stock had shot up more than 40 percent from a 52-week low in April to a more than 9-month high in July amid reports of improved advertising revenues.
However, shares plunged in late July after the social media company's second-quarter earnings report disappointed in the number of new users and showed an 8 percent decline in advertising revenue to $489 million.
That said, the Jefferies analysts still gave Twitter the benefit of the doubt.
Thill said he didn't downgrade the stock to sell because of its recovery in the last two years.
"We believe recent management changes could help improve the declining [average revenue per user] in the near term," he said. "We will pay close attention to advertiser sentiment over coming months and effectiveness of live video."