In the NBA, there's physical toughness, and then there's mental toughness. The 2008 team had both, in droves. They had three physical bench bigs (Powe, BBD, and PJ Brown) who created a meat grinder affect in the paint Those guys, along with KG and Perk, were a handful for opposing bigs.
The bench littles, House, Posey, and Cassell, were guys you could go to war with. That team had a lot of tough minded players in it, and that's why they could overcome huge playoff leads to win playoff games.
Regarding the Celtics bigs, they've been very soft in the paint the last few years. Opposing teams know they can get easy buckets by crashing the offensive boards. You can criticize Perkins for not being a great rebounder, but one thing he does consistently is box out, which besides keeping a top rebounder from the opposing team off the boards, allows his team's littles to swoop in for rebounds. Not having at least one big body who consistently boxes out really hurts a team trying to protect their glass. Sullinger was doing a decent job before he was lost for the season.
I don't know how anyone can watch this Celtics team and not thing that they're soft, both mentally and physically.