One thing to add: TA practice has both a "directorship"/"expert" path but also a regular "partner" path. Therefore I would consider it very similar in that aspect to other industry/functional practices in BCG.
In terms of type of work/cases - transformation and cost rationalization are the lionshare
In terms of culture, specifically for TA, there is a slight difference with the industry practices in the fact that is more global rather than office specific (e.g. a lot of industry practices have informal nodes in specific offices due to the concentration of clients in the same industry near said office). What that means is that you might need to extend your networking outside of London office and take every opportunity to do so (practice events and so on).
Hope it helps,