Amp or DAC?

Let’s say I compare the same company’s 75w into 8 amp and their 150w into 8 amp. Will I notice a difference in sound quality?

Yes.

If so, why?

Not because of power.

If there is a difference between the 75w and 150w per channel amp can I narrow the gap or even exceed the 150w amp by using a better DAC?

Nobody knows. Its a question of sound quality. Power is but one factor- and the most insignificant one at that.

Also, has anyone noticed that a lower watt amp has less distortion than a higher powered one, so throwing my understanding that the same manufacturer’s higher powered amp should be superior to it’s lower powered one out the window?

Often times the lower power one sounds better. Its not about power. Once you get above something like 20 to 50 watts few things matter less. The position of the volume knob. I’ll give you that one.

Different amps perform fundamentally differently; listen for yourself if you don't believe it.

To your second question; No, you can't make a DAC confer the attributes of a better amp, and vice versa. If you want to upgrade the system as if different amp and DAC, you need a different amp and DAC. There are no shortcuts to superior systems. There may be different configurations - but not shortcuts. 

Don't get hung up on distortion specs; it's a great way to build a mediocre rig. 

If you're lucky enough to reach mediocre. The worst sounding system I ever heard was all stuff that looked beautiful on paper. It was also the most money I have seen anyone spend to achieve horrid sound. One night after listening to my system a while his wife came up to me and with this astonished look on her face said, "I could listen to this all night!"  

If that's what you want, drop the thing with numbers. Like a hot rock.

I guess since this is in Tech Talk should probably give a more technical explanation why power is irrelevant.

Music is highly dynamic in nature. Sound is logarithmic in power. What this means, to go even a tiny little bit louder like say 3dB, not much at all really, requires twice the power. Twice. To go 10dB louder, which is enough to actually feel louder, takes ten times the power.

So going from 75 watts to 150 watts, even though it sounds like a lot, is only a measly 3dB. Barely noticeable. Insignificant.

Back to music is highly dynamic in nature. What this means, the vast majority of the time is spent listening to only a watt or two. If that. Theoretically, at least, the only time you are going to hear the difference that extra 75 watts makes is the occasional transient here or there. All the rest of the time its the first watt.  

Because, see, amplifier power is not like horsepower. A car with a lot of horsepower, even when you're only using a fraction, barely crack the throttle, it just feels so much more effortless. You can enjoy high horsepower even without ever using it.

Amplifier power on the other hand, no such luck. There's little 50 watt tube amps that convey a greater sense of power than 150 watt solid state amps. And vice versa. (Probably. Just because I never heard one doesn't mean they can't exist.)

With amplifiers the first watt is so important one of the most famous and well-regarded amplifier designers uses it. First watt. Its so important the great reviewer Robert Harley once said, "If the first watt isn't any good, why would you want 200 more of them?"

And so on. We can get even more technical. We can get into the nuts and bolts of heat dissipation and size and parts complexity and quality. But, why? Harley nailed it.