What advantages or disadvantages will I incur by going to a 19 or 20 inch wheel on a 2014 maxima?

 

For 19's it's not too many. Really depends on the rim

For 20's there are a couple. Depending on wide they are they can rub up against the wheel well. I've heard some say it changes the ride of the car but I say it depends on the tires you purchase. I have dubs & mine rides smooth just like the stock. Also heard it effects the gas mileage but I haven't seen that either. The main important is where you live. If the roads are terrible or you have a lot of potholes I probably wouldn't go with dubs too much of a risk bending them or busting them on a pothole.

All in all it's a personal preference.

 

The bigger the wheel, the more you adversely affect the acceleration, braking, and handling. I'm sure 20" wheels and the corresponding tires cost more than the respective 19" setup too.

 

I'd like to consider myself to be intelligent. That being said I haven't noticed any decreases in mileage, ride quality, or acceleration. I am lowered on eibachs too and I'd argue that the ride and handling is better than stock. But I also prefer a car that doesn't float or bounce when up to speed.
If you're into the mileage game you have the wrong car. The miniscule amount if any isn't worth crying about.
20s look perfect on the car. 19s also but 20s are better imo. If you get a quality wheel and avoid pot holes best u can there's little issue with bending them. I drove up 95 thru NYC with 3 ppl and luggage in my car at 80 mph with zero damage. And I'm on 30 series tires.
Get what makes you happy not what others say you should get.
Ok, getting down off my soap box now.