I think the key difference is the output voltage swing. For telescopic op amp, if you connect the input and output to implement a unity-gain buffer, the output swing is Vth4-(Vgs4-Vth2) [Razavi page 299]. But if you are using a folded cascode op amp, the output swing is higher than the telescopic op amp. Hope this will help. Sorry I am not famillier with the 2 to 1 op amp.
sorry,,,
the 2 to 1 op amp is the differential to single ended configuration.
How about folded cascode and differential to single(D2S) Opamp ?
because folded cascode only open loop gain and Vomax folded is large than
D2S and Vomin are equal .
I don't know what's different between folded and D2S if connect to
Unit gain buffer?