There really isn't one.
Indy has had consistency top to bottom and won in the regular season. But their model is entirely different top to bottom as well. Polian built his team through the draft largely of financial necessity. He avoids FA like the plague and the one year he took a shot at it it backfired, although the team finally won it all despite that failure. Dungy was brought in as a HC who was really a glorified DC (had no choice or say on offense including staff) but eventually broadened his influence and steered the offense towards balanced and a more conservative approach which had been his style in Tampa to create an identity for the unit that wasn't entirely dependent or reliant on Manning, and that too was necessary for them to start winning in the post season.
Pittsburgh has always had continuity by design of ownership. Including reliance on the draft and coaching and little use of FA. And they had pretty consistent regular season success under Cowher over 15 seasons but not championship success until they drafted a real QB (albeit with some warts...). They've become a little more hot and cold since Cowher left, perhaps as a result of said QB, and who knows since Ben's choice of OC has now been sent packing if they will get back to their roots and consistency.
I've never gotten the comparison with Philly. Other than Lurie is from NE... For all the accolades they heap on Reid, he's been nothing like BB on or off the field. And McNabb remains something of an enigma. They had a run of close but no cigar. Lately they are either the odds on pre season favorite or the crashing disappointment down the stretch. Lots of clubhouse drama, too. McNabb is alternately got one foot out the door or he's signing an extension. Ditto Reid. Well, they're both extended now and after last Sunday that's looking like a questionable move. They've used the draft and FA, more FA of late, but so far they have little to show for any of it beyond spurts of contention in most every season. Their forays into rehabilitation haven't panned out nearly as well.
SD is nothing like NE. They rely on the draft of financial necessity, as did Indy, but it hasn't yielded the same consistency although they have had a fairly easy road to hoe of late given the overall dysfunction in their division. Depending on whom you ask they are a top tier talent product of selection with AJ seemingly demanding the credit and their struggles were all coaching related. Norv hasn't had any more success than Shotty to date, though, so that's debatable. Their owner is battling Alzheimers and they can't get a new stadium built in SD and they couldn't fill it even if they did because they struggle to sell games out even when they are the #2 conference seed so...not much similarity there, either.
If you had to pick a team that was most similar even though not nearly that similar, I guess it would be a tossup between Pittsburgh and Indy with an edge to Indy for consistency (although prior to 2007 on the field the edge would go to Pittsburgh on overall style of play which we have recently moved away from on offense). And because unlike Pittsburgh both the Indy and NE franchises of this decade kinda rose from the ashes of being laughingstocks of the league for some time and only achieving consistent contention (after some brief fits and starts) since the present ownership acquired control of the organization in the previous decade and turned football operations over to a disimilar pair of pretty savvy football guys.
