I have seen this argument being thrown a lot around the internet, but as someone who has experienced 4e from the playtest up to it's final days, I just cannot see this as true.
The "sameness" people keeping parroting about is just regarding the resource recharging system, and I don't see it as a bad thing. Now that every class recharge their abilities at a different rate, DMs complain that it's hard to balance an adventuring day without being forced to run eight combat encounters in a row.
I agree. From experience actually playing 4e the fighter played nothing like the wizard which played nothing like the rogue etc.
BUT
They had the same recharge mechanic (as you say) and that immediately led to some people saying either 1) OMG they turned fighters into spellcasters D&D is ruined or 2) OMG all the classes are essentially the same now, it doesn't matter what I play they're all the same! And other iterations of those arguments.
If pressed they'd just retreat into "well, it just doesn't feel like D&D..." and since that's basically 100% opinion there's nowhere to go from there.
it was frustrating to deal with because I thought 4e brought a lot to the table and deserved more of a shot than many people were willing to give it.