All that matters is whether you have the money to build the stadium in one shot. IF you do, then go for it but you spend 18 days and one lump sum for the new stadium.
If you build it by upgrading the stands it still takes 18 days but you can pay for it in installments as you make more money from competitions every day.
YEs, at lower levels, it is hardly worth it for the attendance but at higher levels, say level 7 stadium where I am at, the upgrade is over $15M and thats just about 1/4 of my money. At higher levels, its takes a boatload of money to buy the stadium in one shot, so save your money if you want to do it that way.
Frankly, doing the stadium by upgrades is the smarter way to go about it because of the extra income made in those 13 days after the first upgrade. I am finding that every penny counts the higher level I am, so much so that I have started using the money option on the booster vids in order to get enough money for players and upgrades!!!