Where would stations go on a BD extension to STC? I'd guess 2 inbetween stations; one at Eglinton/Brimely/Danforth and another at Lawrence/McCowan. Would the passenger demand from these stations exceed what is lost at the existing Lawrence East, Ellesmere, and Midland stations, not to mention the proposed SRT stations at Brimley, Bellamy, Centennial College, Sheppard, and Malvern.
I don't think it's fair to throw in the extension stations into the debate between going from Kennedy to STC. There's nothing saying that those stations cannot be built as some other form of LRT or BRT. I see the refurb and the extension as two separate projects, they just happen to be happening simultaneously. But yes, I do believe that the ridership of those two stations would be greater than the current 3 stations in between Kennedy and STC. And there's nothing stopping the TTC from building a buses-only road along at least part of the proposed SLRT extension route, at a cost that's magnitudes less.
In theory, ultimately, it could do both. There is no reason not to have branches. However if the Eglinton LRT get's extended to STC, there is always the option (ultimately) of extending the BD line east with stations at Eglinton/Brimley/Danforth, Bellamy (Eglinton GO), and perhaps even Kingston Road. Though presumably at some point in the far future.
I would think it would be more likely that an LRT could be extended in the future along Kingston Rd, rather than a subway. Routing the ECLRT anywhere east or north of Kennedy basically ensures that B-D will only ever get a 1 or 2 stop extension. I'm not saying routing Eglinton to STC wouldn't work, because it definitely would. Thinking very long-term though, what's the best option? Routing ECLRT to STC would mean that, aside from Sheppard, no subway line will be going any further east into Scarborough, except for maybe a couple new stops along Eglinton east. At least with B-D to STC, there's the option of eventually pushing the subway further east along a pretty major corridor (the 401 and surroundings).