No, inviting online opponents to franchise games was
absolutely not online franchise. Neither was exporting games to files in the PC version and importing game results back in later (I personally don't remember franchise game export to file ever existing on console, inviting an online opponent into a franchise game was absolutely a thing on console starting with Madden 07 though). Regardless, describing either of those features as "online franchise" overloads them with meaning and functionality they absolutely didn't have, including but not limited to:
- a user may load and view a franchise game save remotely without intervention by the league commissioner (i.e. the game save lives on a controlled server, not passing memory cards back and forth or one player having a "master" local franchise file)
- a user may play a game for a given week at any time without intervention by the league commissioner (i.e. a user doesn't have to wait for a commissioner to export his game to a file to play)
- a user may perform roster management functions for his team without intervention by the league commissioner (sign free agents, manage depth chart, cut players, offer trades, etc.)
- a user may only perform roster management functions for his team (i.e. permissions)
- all users may participate simultaneously and remotely in the rookie draft live event
That's the bare minimum for "online franchise" in the correct definition of the term. There were other football games before Madden NFL 11 (the first Madden with any true online franchise functionality, nerfed as it may have been) which met the bar I set above. Simply inviting online opponents to individual games doesn't begin to cover any of the above bare-minimum functionality for such a mode.
I mean, at the end of the day it's all personal preference which game you prefer to play, sure. That said, I personally don't see how one can make any reasonable argument that the PS2 game offers more things and better things to do than the current game for the reasons I listed above. There is no feature of the PS2 game on the field or off it which is more robust / well-designed / truer to the real-life NFL, the PS2 game has fewer and shallower gameplay mechanics to master (even getting to core basic stuff such as making a tackle), the PS2 game has fewer modes and ways to play, the modes which are shared between the PS2 and PS4 games are ten years behind on PS2 with respect to gameplay balance, the PS2 game doesn't offer any reasonable on-boarding assistance for new players, and the total package is less cohesive. It is objectively inferior in every possible capacity.
Doesn't make it a bad game, per se - it was a good game for its time - but it just doesn't hold up when graded against modern expectations.