They really serve two different functions. Tripwire and similar tools like aide (I use aide now rather than tripwire, but that's my personal preference, I'm not

They really serve two different functions. Tripwire and similar tools like aide (I use aide now rather than tripwire, but that's my personal preference, I'm not an infosec domain expert) are file integrity checkers that check files for property changes (including mtime). Tuning out false alarms can result in an admin just turning off the reporting functions of the tools, that's the downside as I understand it. However, rkhunter has additional logic to specifically seek out rootkits and malware-like behavior, and is more specifically targeted to system file modifications. Combining it with unhide (to compare actual processes running with those visible from userspace) provides a reasonable assurance that nothing nefarious is going on. They're all part of a spectrum, however. I use scanners like aide alongside rkhunter as well, but I'm the sort of guy that will spend a day tuning the config of aide to avoid constant false alarms.