I suspect my iPhone has issues with the GPS but these are noted problem with phone GPS's in general. The iPhone (and any phone's) GPS is not going to be as accurate as a standalone GPS. It's a crummier antenna for GPS and it has a lot of other stuff going on in the case that can impact receiver sensitivity.
For biking, compared to the Garmin units, for example, the vertical positioning and changes are far different. The Garmin is pretty precise and accurate. On one ride, I do, it shows a net change of 246' over the ride (pretty flat and correct). The iPhone shows it anywhere from 1000' to 7000' and grades that I climb of up to 46% - obviously wrong. The reason for that is partly my not great iPhone GPS, but the Garmin 705 also has a sensor for barometric pressure to deal with the micro changes and the iPhone doesn't have that.
But this will get ever better. I like the idea of not having to use a separate bike computer since I have to carry my phone with me anyhow.
I doubt there will be any difference in accuracy between ANT+ or BT. Given the choice, I'd take the BT just for the battery savings. I would suspect that ANT+ will phase out over time in the face of BT being a far more useful and practical standard long term.