To the fist question, if both amps are making the same power into the same load the current will be the same as well.

The higher powered amp will be capable of more current at higher power levels.

'High current' amps are usually those that can drive 4 ohm loads with double the power that they make into 8 ohms. This characteristic is also known as 'constant voltage', i.e. the amp is regarded as a voltage source. What this means is it can make the same voltage regardless of the load. So if the voltage is the same into 4 ohms, the current will increase such that the power is double that of the 8 ohm load, given that both loads see the same voltage.

Now if you are still with me, the real question is, 'is that important for musical reproduction??' The answer is a qualified 'No'. IOW its important for some speakers, and other speakers sound worse if the amp has that power doubling (high current, constant voltage) characteristic. You have to look at the intention of the designer of the speaker to sort that out.

If the designer uses tube amps, its likely that a SS amp that can double power will not exhibit flat frequency response on that speaker. OTOH if the designer did use a SS amp with his speaker, then 'high current' might be useful.

More:

http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php

The higher powered amp will be capable of more current at higher power levels.

'High current' amps are usually those that can drive 4 ohm loads with double the power that they make into 8 ohms. This characteristic is also known as 'constant voltage', i.e. the amp is regarded as a voltage source. What this means is it can make the same voltage regardless of the load. So if the voltage is the same into 4 ohms, the current will increase such that the power is double that of the 8 ohm load, given that both loads see the same voltage.

Now if you are still with me, the real question is, 'is that important for musical reproduction??' The answer is a qualified 'No'. IOW its important for some speakers, and other speakers sound worse if the amp has that power doubling (high current, constant voltage) characteristic. You have to look at the intention of the designer of the speaker to sort that out.

If the designer uses tube amps, its likely that a SS amp that can double power will not exhibit flat frequency response on that speaker. OTOH if the designer did use a SS amp with his speaker, then 'high current' might be useful.

More:

http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php