what are the pros and cons of either amp power specification?

In many ways your question is really about which sounds better, your average tube vs. your average solid state amp, whose output vs. impedance profiles are as you describe, and there's no simple answer to your question in terms of which is preferable.

We can usually assume that an amplifier that does not double it's power as impedance drops has higher output impedance. This is not always, inevitably true, but mostly true.  Sometimes an amplifier can maintain a flat frequency response any time you stay below it's maximum output, though this tends to be rare, but possible with high enough feedback.

When an amplifier has high output impedance the frequency response changes from flat to one that looks like a speaker's impedance curve.  That is, the impedance curve dominates the amplifier's output. Take a look at any tube amp measurements from Stereophile which uses a simulated speaker load to see what I mean.  Here's an example:


https://www.stereophile.com/content/cary-audio-cad-805rs-monoblock-power-amplifier-measurements

The squiggly black line is the output changing from flat-ish to the speaker impedance.

Is this bad?  Meh, depends.  Sometimes you get a great combo that really colors the sound in a way you find pleasant.  Sometimes it means you want a speaker that has a really flat impedance curve (like Fritz) so it can be more neutral. 

If it’s Solid State output-transformerless, then being rated the same power at 8 ohms and 4 ohms is generally NOT a good thing. It typically indicates that the PSU and/or output stage and/or heat dissipation is not robust enough to handle the increased demands of a 4-ohm load - and that’s not good because it can certainly affect performance even on 8 ohm speakers (also realize that most speakers are not a fixed impedance across all frequencies - far from it, in fact). The "gold standard" is for an SS amp to "double down" its power when you half the impedance. Then you get to tack on extra buzzwords like "load invariant" and "high current", etc.

So the Sprout displays that nice doubling BUUUUUTTTTT...realize that some manufacturers may goose the numbers to make an amp look like it doubles down perfectly, when it doesn’t. For example, consider an amp that makes 250 Watts into 8 ohms and 400 Watts into 4, by some standard of clipping (typically 1% or 10% distortion level). The amp maker might decide the market will be more receptive to a 200 Watt / 400 Watt amp, so they could purposely spec their amp as such - technically they’re "under-rating" its power at 8 ohms to make it a clean 4-ohm power doubling on paper. Why does this matter? Because when you put this amp on a 4 ohm speaker with a dip to 2 ohms in the bass region, this amp may run out of gas (so to speak) compared to an amp that actually doubles 200/400/800Watts into 8/4/2ohms. Never buy amps from tricksey hobbitses lol.

Tube amps and autoformer-coupled SS amps (like McIntosh) are a different story. Then there's the matter that a particular speaker may have been voiced more for "load invariant" amps or for "constant power" amps. 

* And yes, sound quality considerations are a different matter, but generally amps with compromises in PSU / output stage / heat sinking are at least correlated with less than stellar sound quality.

rlj

What are the pros and cons of either amp: 1) an amp that is 100watts at 4 ohms and 50 watts into 8 ohms or 2) an amp that is rated at 75 watts into either 4 ohms and 8 ohms speakers?

In a word: Nothing. Taken by itself, the spec doesn't tell you how the amp will sound.

Good answers

Best performance not Always = best sound. Best sound is totally subjective. But you have a better chance at best sound when performance is good.

So if you have the typical modest load speaker that would probably make me lean towards the amp that increases power into a lower impedance for best performance ie lower distortion At least based on specs which tend to give at least a clue about what to expect even if juiced somewhat.

The one that doesn’t could still sound better and may even perform well if the speakers are designed to be an easier load.

So its always an educated guess until you actually try and find out. Some educated guesses are better than others. But you have to decide somehow which to try that has best chance to sound good.

Best would be to try different options and see. Unless you get it right the first time. It happens.  Chances are best with a highly educated guess. 

It depends on the load of the speakers the amp will drive.

This subject was covered exhaustively in a 1981 documentary that gave it all the seriousness and respect it deserves:  https://youtu.be/6iCbK3ooekU?t=24

I missed typed the Sprout100 specs its 100Watts into 4 ohms and 50 watts into 8 ohms which I'm comparing to the Bluesound POWERNODE2021 power output.