I can't think of a practical way to integrate the ramps/approaches into the south end for a bridge long enough to cross that distance and high enough to allow ships to pass underneath. A tunnel would be the only practical option even though we'd be losing out on having a grand landmark. A tunnel would be more costly and it wouldn't have as much capacity but really the street grid wouldn't be capable of handling huge amounts of traffic dumped in that part of town. Given how much NIMBYS holler about how any new building would change the "character" of a neighbourhood, just imagine how much the introduction of traffic from a multi-lane freeway would change the character.
But honestly, if we're serious about a third crossing we should be considering a rail tunnel with a light metro service. We already have two road bridges so the argument about having to have a backup in case one is blocked... well we already have a backup. Each is the backup for the other. And if we're worried about development patterns of the HRM, the argument isn't just about car commuter oriented development in one part of the region vs another as if car commuter oriented development is the only possibility. If a rail connection is the fastest and most reliable way to get into town and enabled people to avoid congestion, then that would inevitably affect development patterns.
When we consider the amount of infrastructure and functionality we'd be getting relative to the money spent and overall effect on the community, then a BART style trans-harbour tube would be by far superior. Vehicular tunnels are extremely expensive because they need to be much larger - especially if they're to carry transport trucks - and need to have much heavier-duty ventilation systems and fire suppression systems. Not to mention that a tunnel connecting the circ to the S. end would need to be longer than one connecting the two downtowns 1.3km vs 1.7km. The amount of funds needing to be spent on a 4 lane road tunnel and approaches could easily pay for not only a metro tunnel that extended under the harbour, but one that also through the city.
In terms of affordibility, we if we afford the road tunnel despite its fewer benefits we can afford the metro option. The metro option could also be paid for by user fees as most transit services charge as fare anyway. It's important to note that while many transit agencies have a farebox recovery ratio of well under 100%, that is for their operations as a whole which include highly subsidized bus services on lower ridership routes resulting in a relatively low number of riders per driver. When we look at subway/metro lines of many transit agencies on their own, it isn't uncommon for these services to be revenue positive allowing them to actually help to subsidize the rest of the system. Our metro line would be automated like the Vancouver Skytrain or Copenhagen metro making it extremely efficient. Also, we can't just look at it in isolation. Such a system would also allow many buses to be taken off the road and out of inefficient congestion.
Here is a brief diagram of the route, with oragne sections being elevated (the two branches in Dartmouth) while the red (main) section wold be tunnel, while the yellow section is surface. I envision it as having 30m long vehicles and peak headways on the combined section of 15tph or 4 min to start while the off peak would be 12tph or 5 min. Obviously these could be increased as warranted by demand with maximum throughput being about 34 tph or ~1:45 min.
I would keep the Woodside commuter ferry, but the Alderney ferry could be discontinued or just run infrequently in the summer for tourists. The main Dartmouth transit hub would shift from Bridge Terminal to Alderney, while MicMac and Tacoma would have major park'n'ride garages in addition to the bus connections. This along with the number of bus trips that the service would save would reduce costs hugely and take more loud and polluting vehicles off the road than would removing transport trucks from downtown with a road tunnel.