I cross the GWB if I'm in a rush otherwise I would take 287 to 87 to 84E into CT. By the way, crossing the GWB is no different than crossing the Tapp other than a larger toll. You can hit traffic at either. If you take 287 to 684 time it out to avoid rush hour on 84 through Danbury, CT between 11am and 2pm would be best. During this time period you will also avoid the worst traffic in Waterbury & Hartford. We have a home in Danbury, I'm on these roads daily during the summer months.
If you do hit traffic in either city it's best to stay in the left lane to avoid merging traffic from several on-ramps. Exit 2 in Danbury has a very nice recently renovated rest area with overnight parking and a public dump station.
Safe Travels!
Rob