Cindy, general-entry tickets for the Colosseum/Forum/Palatine (1 ticket covers all three) are not time or date specific. You can use tickets you purchase today on any day the sites are open until the end of this year. The tickets you would purchase on the rome.info website won't be of any advantage as they don't allow you any quicker entry than those bought on the coopculture site: they're both general-entry tickets.
Both allow you to skip the ticket line
Neither allow you to skip the security line. As stated on the rome.info page:
"Skip the Line tickets allow you to skip long waiting lines at the ticket office, but does not exempt you from security controls. "
Same with coopculture.
42 euro = $45.82 in today's conversion so why pay more?
Adding: the rome.com site says "With the ‘Ticketbar Combi-Deal’ you also get access to the Palatino and Roman Forum! " That's no "deal." The same applies to tickets bought from coopculture or at the Colosseum/Forum/Palatine themselves so it's a fine piece of misleading advertising. A good reason right there, IMHO, not to use that site.