One aspect of TT vs. Mint is that both are from Intuit. If you trust Intuit, with which many of us are perhaps having problems, then TT and Mint are probably equally safe from the perspective of data security.
Another aspect is the nature of the info being provided. TT has personal info, SSN, and snapshots of high-level asset info. If you use the desktop version of TT, there's a possibility that much of that info does not go to Intuit. I would hope not, since it's not needed by Intuit. However, Mint has financial account username/password and downloads account details. I haven't used it, but I work at a financial institution with close involvement in authentication where it's clear that Mint frequently downloads automatically and possibly on-demand as well.
Another issue is the chance of forgetting that you signed up for Mint, changing your password, and having Mint continue to try logging in with an invalid password. That can lead to account lockout at some institutions. It's certainly caused major issues from my experience, requiring technical changes to reduce the impact on users - especially those who infrequently login manually.
