How come we have dfferent current delivery for the same watts
You don't, Watts = Volts delivered by the amplifier across the speaker load. Change the volts or load - which will change the current demand - to change watts.
I have seen big transformers and high capacitors rating in one amp and the other smaller, all with the same wattage.
Bigger transformer with the same ratio can (probably) deliver more current to the storage capacitor in a traditional design (I don't know SMPS)
Output section draws from the capacitors.
Same voltage (maintained by current flow) across same load = same watts.
Am asking why that information is provided by some and not others.
Some amplifiers will have the ability to drive lower impedances. That will require more current for a given output voltage. Some amplifiers may be specified down to a 1 ohm load. That requires more current from the storage capacitors, so the capacitors will be "bigger" and the transformer will have to deliver more current to them to keep them charged between charge cycles. The capacitors only charge near the peaks of the AC power input, and drain during the rest of the AC power cycle.
Sometimes some of this information is given, more often when the amplifier is designed for more difficult loads and, perhaps, high power output.
Mine are specified for 2 ohm operation and 1400W. That would imply 53volts rms, 26.5 amps, which is a rather demanding spec. Maximum voltage across the speakers is specified as 138Vpk
I want to see the wattage and current delivery to help make a decision.
You'd also want to know the demand of your speaker load, the sensitivity of the speaker, and the volume levels at which you expect to drive them.
Note: 1 watt is usually pretty loud. You probably couldn't listen to a 1 watt tone very long without ear discomfort.
My proxy measure to judge if the power supply of an AB amplifier is beefy enough is the weight of the amplifier.
50+ pounds per channel (monoblock) here. Spec says 68, but I think it's wrong.
It has a "big" transformer, but the storage caps aren't particularly large. It has a regulated voltage supply (uncommon) for the rails, so less dependency on low ripple from the capacitors, I presume.
My other amp is a more basic design, has much more filter capacitance (unregulated).