You should shoot at 10mp because that is the best image quality from your camera!
As for your original question, it depends. I think the biggest most noticeable difference to make comes from better lens quality all else being equal.
The sensor matters for a whole gamut of reasons pixel pitch, density, bayer array, x-trans, foveon, CCD, CMOS, crop, full, medium format, BSI etc. mega pixels is something that the sales people in the chain camera stores have used to sell on for years. The reality is that unless you are printing big, and you want to look up close, then the mega pixels dont add much to the pixels per inch argument. Take a billboard - a billboard is viewed from a distance and they are mostly images in the 2-3 mp range but as you know, stand 4 feet away as you would a picture on your wall and they look horrid.
I think the CMOS sensor industry has been consolidated now and we see that actually there are only a couple of actual sensor manufacturers and they sell them to multiple camera manufacturers so the magic happens in the software in the algorithms for getting the image from sensor to image file.
When it comes to taking images from your Powershot vs the iphone, it is a much argued conflict. Some people on here -
@akash.nu for example has kicked my ass for years using his iphone to demolish various camera combos I have used. The largest element of the equation is who is wielding the weapon.
@Apple fanboy has beat the snot out of my foray into Sony with his rickety DSLR Nikon
p) as has
@mollyc who has me looking at my now Nikon and throwing tantrums because I am not getting anything like the quality of the shots she gets from hers.
Wow off on one again.
When it comes to lenses, and we think of quality of optics, we may think of Canon L series and Nikon or Zeiss and Leica (the last two are amazing btw). Actually though, Fuji are arguably the best lens makers on the planet. Fuji make lenses for NASA, Fuji sell a $50,000 TV camera lens perfectly corrected with no focus breathing but in the camera place we often discount them because they dont tout L series, APO, Aspherical etc....
Sorry still off in the weeds....
Back on point.... I think it is a dimishing returns scenario. I think for 99.999% of us, a 24mp full frame sensor capable of clean shots at 3200 ISO with a decent 3 lens trinity (zoom or primes) is about the best we need. Beyond that we are getting into nuances and specific benefit use cases at which point each step of added magic costs exponentially more than the last.
The common point we all know to be true though is that a camera is a tool and knowing how to use it trumps the go faster stripes and the turbo.
Now..... here is the other thing to consider.... as every camera and manufacturer approaches perfection in image reproduction, colour definition, clean noise free detail rich images..... then we start to crave flaws in the name of character, as a means to stand apart. I love a certain manufacturer for a reason, I use their old cameras for a reason - they are different, they are not perfect, they are annoying but you know what? when you nail a shot, nothing touches them.
Hell right now I am obsessed with making my images from a full frame sensor camera look like the images from a Holga! I should just save a fortune and get a bloody Holga - zero megapixels, infinite joy.....
Erm, sorry...... totally went down a rabbit hole there...