I don't think they are. Unless you argue Bedser is like O'Reilly. Who was again different to your classical leg spinner. It doesn't matter if they were similar. For a batsman it would be like facing no peace from both ends. I think Faulkner's bowling record a bit patchy though he is definitely worth a spot in this team, no doubt. Just can't fit him in, especially over two players whose reputation is greater than his.
Bedsters stock ball was medium fast swing, with the variation of cutters. His cutter sounds like it was a lot like Barnes legspinner in effect.
The other three had a legspinner as a stock ball, with various degrees of variation. I think we can lump the three of them together in different class to Bedster on a scale from closer to modern legspin in Faulkner (used flight sometimes) to further in Barnes (started as a quick, added offspin then legspin).
Faulkner was definitely, for his era, a worse bowler than the other 2. His skills might translate somewhat better into the era of covered pitches due to mostly bowling slower, but it's difficult to know and extremely difficult to argue he would have been a better bowler.
Barnes I think would have succeeded in any era- you don't need much movement to be successful when you are bowling in the 120kms. See Vernon Philander bowling seam. And he could always change bowling styles as needed.
Tiger would likely have been significantly less successful. See Jadejas home and away record for faster spin. He may still have been a better bowler than Faulkner though, but the argument for Faulkner adding balance is based on his batting, not his bowling. He was ranked the number one bat in the world at one stage (as with his bowling). This is a team playing 5 bowlers, and a wk who isn't Gilchrist. It would definitely be a better balanced side by including Faulkner, whether or not you think it would be a stronger side.
Barnes's reputation is definitely greater than Faulkners, but O'Reilly's isn't. He may be better known (not sure, I'm south African), but he wouldn't be more highly thought of by those that know them both. O'Reilly is an elite spinner, but there are a number of bowlers in his tier, whereas Faulkner is the only elite spinning allrounder, and arguably the only balanced allrounder to have ever played tests.