Saeco owns Gaggia. Having said that now Philips has bought out Saeco.
They are two different machines. Saeco uses the pressurized portafilter to make coffee. Gaggia has much higher wattage and an industry standard 58 mm portafilter so if teamed up with a good Italian espresso grinder you will get some decent shots with it. The saeco will give you faut crema as the pressurized portafilter manufactures it. Coffee connoisseurs would take the Gaggia route for the better taste ... others may take the Saeco route.
In a nut shell that is the difference between the 2.
I have an Aroma, and have removed the pressurization component of the PF (a very easy and neat procedure).
It is now producing a very nice thick crema, and as an added bonus the PF is now easier to clean.
No need to discount the Saeco based on the pressurized PF