No cons, but no pros necessarily either. "More power going in" isn't any advantage if the speaker can't use it... and if your speaker needs more power (especially in a free-air setup like a door), that's not necessarily a good speaker. I'd have lots of questions about it, and why I couldn't drive it to full output on the 4 ohm level of power. Of course, that also assumes we're talking about an otherwise-identical comparison - a 4 ohm speaker that left you wanting, so you bought the 2 ohm version... which doesn't really exist in the midbass world. My point is - "more power" has no intrinsic benefit.
You want the appropriate amount of power to drive the speaker to full excursion.
And if that's possible with, say, 50 watts at 4 ohms, why would you swap in a speaker that required 100 watts to do the same thing?
Same things with subwoofers - I hear people bragging all the time about how a sub can handle over 1000w - "that's impressive!"
No, it's not really. It's a big, fat, heavy high-mass winding that's increasing moving mass to the point where it NEEDS nearly 1000w just to get loud. If you could get the same excursion and output with a sub that only needs 200w - THAT's the more impressive subwoofer.
(just like I wonder all the time, how so many people today are totally OK with thinking they need a 2000w+ amplifier, upgraded alternator, extra batteries, etc... just to drive a couple subs - and apparently aren't bottoming them out! Tell me THAT doesn't raise questions about the most inefficient system ever...
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All that matters is what matters - that you are driving your speakers cleanly, and are getting full output out of them - that your amp (at whatever impedance) can drive them to full excursion. People focus on the stuff that doesn't matter - or worse, praise the stuff they don't understand (triple-stack magnet, anyone?) - a whole lot.
And I don't mean you, this is a great question to actually start a deep-dive into some real understanding.