The CDD guys are about 25% of strat headcount, but even they are mainly doing Strat work at the moment.
There are relatively fixed demarcations between the industry teams, with PS and HCLS having a very different feel to M&A and CB TMT.
I would say that if you want real strat, there is some at Deloitte, but it is mostly in the CBTMT space. PS Strat and FSI are quite operational. M&A is (used to be) very CDD focused - which is also quite strat-heavy - lots of analysis; competitor/ customer / market / firm etc - a compressed microcosm of many larger strat pieces.
Dont be put off by shallow remarks about the colour of a shirt. "I met some of the team a year ago" essentially means "I was invited to interview and couldn't make it past the first round, and am now reduced to making embittered, shallow remarks that reflect the complete lack of substance that probably ruled me out of a job in the first place".
Of course Deloitte strat is quite average as far as strat goes - if you want above average, or brilliant people to work with then you know where to go - MBBB etc. However, if you want to do a mix of strat work, with the opportunity to rove around across a large practice of >200 people, with a healthy balance of shorter days and interesting client projects, you could do a lot worse. My main gripe would be the pay.