How important is Amplifier Continuous Power matching with Speakers nowadays?

Power rating on speakers is nothing more than a general guide to how much power the speaker can handle without burning out. It has nothing to do with how good the speaker sounds or even with what amplifiers it can be used with. 

Power rating on amplifiers refers to some very specific measurements in which the amplifier is very thoroughly warmed up and then measured and can put this amount of power out on a steady basis without distortion. It has nothing to do with how good it will sound or what speakers it can be used with.

Using either of these is a good approach if all you care about is being able to blast as loud and as long as possible, and nothing else. Then by all means go for it.

I doubt it, since your first sentence says you are upgrading looking to get better sound quality. But then all the rest has nothing to do with sound quality. So it would help a lot to know your priorities.

You don't have to worry that an amp is too powerful for your speakers. That's not a problem. It's a problem if an amp isn't powerful enough for the speakers because then it will clip and that's what destroys speakers. An underpowered amp.

Hey yes 100% the question isn't focused so much on the sound quality, that's just the reason I want a new amplifier. I am just worried that if I run an amp with a continuous power of say 200W or 300W into a speaker that has the following power rating if there would be a chance I damage the speakers?

JBL L830 - Power Rating - 75W continuous/300W peak

My speakers are rated at 300 Watts input, my amps are rated at 600 Watts continuous output and the sound is magnificent. When I have it really loud the amps are putting out maybe 5-6 Watts. As hombre said, not enough power poses a danger to you speakers.

Thanks guys, makes me wonder what the point in max continuos power ratings on speakers are for then?

Given the choices, if cost affordable, that NAD M33 looks very desirable (for your young digital loving crowd). 7" lcd control panel, features galore, high quality, slots for future technology.
200 wpc into either 8 or 4 ohm loads is very nice, plenty of power for the majority of speakers.
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MINIMUM watts per channel needed is the most important factor regarding speaker damage, too little can harm speakers. The speaker’s sensitivity determines that, see below.

MAXIMUM watts per channel is not meaningless, but is essentially meaningless, you could but wont burn out a speaker with too much power (except by intention while wearing earplugs). Yes, some drunken teenagers could blow a tweeter, but .....

PROTECTION: NAD still has protective circuitry doesn’t it? I seem to remember NAD’s initial claim to fame in early 70’s was it’s ’soft clipping’ protection. That allowed the safe use of borderline low powered amps, physically smaller than otherwise needed. McIntosh amps have protection built in, other brands must also, read the specs.

ENOUGH watts per channel is important, for Instantaneous power for needed surges of volume (any frequency) in the music, and if trying to produce a lot of bass: lots of continuous power is needed. Buying more power now gives flexibility when considering alternate speakers in the future.

SENSITIVITY (efficiency) (how loud compared to other speakers?)

Standard measurement to establish a COMPARABLE # is a mic 1 meter away, a 1 watt signal sent to the speaker. What sound level in decibels (db) produced by THAT speaker? ____ db? That is the primary fact you want to know about a speaker when choosing MINIMUM NEEDED wpc. Those JBL 830’s Sensitivity is 90db, placing them in the average sensitivity category.

meaning: measured 1 meter away, given only 1 watt of power, they produce 90db sound level.

A less sensitive speaker, say 87db rating, would need more power to produce an equally loud 90db.

https://www.psaudio.com/article/how-much-power-do-i-need/

excerpt

"Basically, you need one hundred times more power to get another 20dB in sound pressure. That means if it took one Watt to make 90dB, it’ll take one hundred watts to make 110dB (and 115dB is as loud as a rock concert)."

a bit more here

https://www.musiciansfriend.com/thehub/understanding-wattage-speaker-efficiency-amplifier-loudness

Hi,
more power does not harm speakers.
Too much power on very sensitive speakers is questionable in terms of sound quality.