For racing tandems or hard-core training rides where stops are infrequent, no question that road pedals and shoes are a good choice. However, for all other forms of tandeming I strongly advocate MTB shoes and pedals.
First off, as you note, the lugged rubber soles of the MTB shoes provide you with firm footing for starts, stops, and bike manuevering.
Secondarily, I find that riding tandems becomes a much more socialized activity and tends to involve a lot more walking around. MTB shoes are far more adaptable to that walking around than road shoes and pedals.
FWIW, we used SPDs for about 14 months and switched to Speedplay Frogs about 7.5 years ago. SPDs are a bit more compact, don't require Dremmel work on the soles of your shoes, and don't become exposed to the ground as readily as the Frog cleats but I've come to enjoy the float afforded by the Frogs. The slight exposure of the Frog cleat beyond the lugged sole has never caused me to lose my footing, but have occassionally scuffed the hardwood floors in our kitchen.
SPD pedals also seem to be a bit more durable than Frogs, but Speedplay has been outstanding with their factory support and inexpensive rebuilds when a pedal occassionally develops a problem.