I've been googling around, some places claim that the transit apps will plugin and be displayed within maps, others claim that it will simply launch an external app. However things seem to be slanted towards launching external apps.
It's a little disappointing from a UI perspective, but honestly I'm still not bothered.
Remember that app I mentioned earlier, the one I wasn't sure if it could handle the London underground? Well I tested it out, yes it can handle the underground and busses etc. It showed me a train journey from where I live, into London, then it showed me multiple ways through London and then a train journey from there on out.
Admittedly this is a UK app and not New York, but surely something similar exists or will be created very soon.
This was the OPs main complaint, that the new transit apps wouldn't be able to calculate routes involving multiple modes of transportation, that a separate app would be needed for each mode (one for bus, another for subway, another for bike ect) however I find it more likely that a developer will release a single app called "New York", covering all available modes of travel and working out the best method. Apple created a gap in the market, then put a big red flag beside it to attract developers.
Is the current app a downgrade and lacking functions present in the current app? Yep. Will this be a problem in a few months? Doubt it.
The lack of street view and spotty flyover coverage are more of a concern to me.