Of these two, Telegram is hardly verifiable: its clients are open-source, BUT the sources in the public repository are updated very rarely, so if T. wants to slip in some malicious code aimed at a specific user to compromise their Secret messages, they can very well do it in a number of ways.
But, given that the vast majority of Telegram users do not even user the secret chats, they can just accest all their chat history without any efforts. Since you can log in to your chat history with just a login and password, the even if chat history is indeed encrypted 'in storage', it is clear that Telegram can decrypt your messages for you. Consequently, they can decrypt it for themselves or for anyone else. (I personally think that they don't even bother, what's the point of doing extra work if nobody sees that anyway?)
Thus, the only thing that users can rely on is Durov's reputation, as a fearless modest person with few material possessions, who was pressured by Russian government to sell his business to Putin's cronies. And here is the problem:
Rosenberg in his series of posts alleges a lot of things. First, that Durov has quite a few material possessions, of which he lied (not a big deal in itself, but it adds up). Then, Durov has lied that once he launched Telegram, T's developers were located in Germany. But they turned out to be working from the same office as his old business, which was taken from him in a rather hostile way. These allegations were never addressed by Durov, the only comment he made was the attack on Anton's personality ('This man is a jerk', basically), and Rosenberg has even won his case in court, proving that his claims for payments, etc were solid and he really did work for Telegram in Russia. Do you have a feeling that Durov's reputation is kinda besmirched by now?
Then, this famous case when Russian censorship agency, Roscomnadzor, has tried to ban it in Russia, and couldn't. For some reason, the most obvious thing you do when banning an app was not done: Telegram had remained on Google Play and Apple's AppStore. We know that Google and Apple have previously complied with Russian government requests to ban apps (as proven in the case of Linkedin), but with Telegram it wasn't done - and all sources claiming that Roscomnadzor has demanded the ban were sourced to Roscomnadzor's own post (I have personally verified about 40 news articles, they all linked either each other or RCN's post) - and it is unclear if this demand was ever officially sent to Google/Apple, neither of them have ever confirmed or denied it. (btw if somebody has a congressman or district attorney pal, it would be good to send an official inquiry to Google and Apple to put this question to rest! Anyone?)
And then we have the 'unban' of Telegram by Russian authorities. This is in itself is unprecedented, for a russian government agency to back down from earlier demands 'because they were unable to make it stick'. Nothing like this has never ever happened, russian government officials just don't function like that, under no circumstances! And the week after the ban, Telegram's top manager sat on the same board with russian government officials! This alone makes me think that all this 'telegram's ban' was a successful special PR operation to build up Telegram's reputation, at the expense of Roscomnadzor reputation, which is below the lowest anyway.
So we have questionable reputation by Durov whom we know to lie about vital things, and we have very suspicious block-unblock story, and nobody really knows anything about Telegram the company and where it is incorporated, etc.