I wonder if they're reputations would have stood up to the media scrutiny of today.

Probably they actually would. But neither of them would get their party's nominations today.

I read one of Eisenhower’s biographies and he actually had some problems with the press especially thanks to Montgomery. At the same time, he was also one of the first US presidents to recognise that news can be leveraged to spread your message. Unlike earlier presidents, Eisenhower actually cooperated with the press and gave them news directly. That together with him winning a major war for America makes me suspect that his reputation would have also stood up with the media scrutiny of today. Assuming that there even is more scrutiny today? Maybe because there are more journalists nowadays so yes it could be

You think Obama was dishonest?

Yes, definitely. I was infuriated by many of W's policies regarding war and domestic spying, and Obama said he would stop those abuses, but instead continued on as was, or worse.

I think generals have an important advantage in honesty. No matter how political an officer's life is, it pales in comparison to the amount of lies needed to be a career politician.

Grant was also known for his unlacquered honesty. And for his desire to serve the nation. Whereas Lincoln changed opinions when favorable to him and was happy to suspend rule of law for the same reason.