Based on a quick look at the data sheets, the parts are not drop in compatible, but could be used in the same footprint with some changes.
By default the reference voltage is the same (2.048V), but the output signals are not. The 1655 output is scaled to 2x the reference voltage. The 1257 output is scaled to 1x the reference. If you use the 1655L, which is referenced to 1.25V instead of 2.048V the output amplitude will be similar, but not the same. You could also give up 1 bit of resolution and only use half the range of the 1655 output.
The 1655 can only be powered by 5V and the reference must be near Vcc/2. The 1257 can be referenced to 12V.
The 1655 is rail-to-rail so it can drive the output voltage from nearly 0V to nearly 5V. The 1257 can only drive the output voltage to Vcc-2.7V. Both would be considered "single supply" since you don't need a negative voltage supply.
Steve Turner