At rush hour a subway on Eglinton and Sheppard ought to be at least comparable in speed to driving on the 401. Let's assume that building subways does not reduce congestion on the 401 significantly, because anyone who switches to transit from driving on the 401 is replaced by new traffic (probably true). A subway goes about 30 km/h and due to traffic congestion the 401 can often be slower than this in rush hour. A subway or underground LRT on Eglinton will definitely be faster than driving because Eglinton is congested all day long 7 days a week. I am pretty sure that if driving and transit take about the same amount of time lots of people will take transit, because driving in heavy stop and go traffic is no fun at all, though lots of people will drive anyway.
A LRT on Eglinton, as long it is well designed (like Calgary LRT, not St. Clair) should be only slightly slower than a subway, the big issue is capacity. With headways constrained for 5 minutes for the line to run efficiently and shorter trains than a subway, you are limited to 1/4 the capacity of a subway which means that the line risks being a victim of its own success and becoming overcrowded. Sheppard on the other hand will be a lot slower because of the transfer at Don Mills/Sheppard (5 minutes wasted), and the lack of connection to Scarborough Centre (people going there will have to either transfer again, or avoid the Sheppard LRT and use the York Mills bus). I have a strong suspicion that the trip from Scarborough Centre to Yonge/Sheppard by TTC will take LONGER than it does now due to the elimination of bus #190, if the Sheppard LRT is built.
The only way to build a rail line that is a lot faster than driving in rush hour would be to buy the CP main line and run trains every 5 minutes on it. Convincing CP to sell this line to GO will be hard, and this line would only stop at major stations so you still really need a subway on Eglinton and/or Sheppard as well to serve the more local stops. This line could take a ton of people off the 401 but connections to Eglinton and Sheppard at Sheppard/Kennedy and Eglinton/Leslie are absolutely essential. Lakeshore and Georgetown GO might take a bit of traffic off 401 as well but are too far from the 401 in most areas to make much of a difference.