I wouldn't count t20 and neither would any serious lover of the game but ODI cricket has been counted as part of a great cricketers career for a long time. It forms about 40% of Tendulkars legacy and a similar chunk of Wasim and Waqars legacies. I don't see how this is even up for debate.
Now, onto the rest of the discussion. Jimmys turn in ODI cricket is respectable and like I said, saying mediocre was probably harsh but he is far from great in ODIs. His number of wickets is testament to his time in the ODI game, spanning some 13 years (I know a few were spent out of the team). Once again, Jimmy has grafted in terms of longevity to achieve those numbers, which have not come through greatness. It's very much like Bernard Hopkins and his legacy as opposed to Ray Leonard.
In terms of Freddy, he averages less than 25 with the ball and consistently bowled at 90 or more mph. If only his test career was stronger and his batting better, he'd be a lock as a great all rounder. Certainly a more valuable English player imo than Jimmy. The same goes for Swann, especially to average under 30, as a spinner. Oh and England can't have won their only ICC tournament if it wasnt for a certain KP.
Look, none of this is to say Jimmy is bad, in fact, he has been one of my favourites for years now. A very skilled operator, a fine swinger of the ball and a terrific example of fitness and longevity in sport. But if I take my personal opinions out of it, he doesnt isn't an atg. An English great certainly, maybe even a 21st century great if I'm pushing it but not all time.