I did consider the Mazda 3 when choosing my next hatch, bear in mind I was slightly biased coming from a series of VW Golfs.
The Madza 3 has quite nice exterior styling, it looks sportier than the Golf but tends to look much like the other Asian brand hatchs from some angles. I found the interier to have a cheap plasticky feel to it and a lesser quality feel compared to the Golf. I also preferred the Golf layout and logic behind button placement (this has been carried through various gen of Golf).
The back seats of the Mazda 3 felt cramped and less spacious, plus no rear HVAC.
The all round visibility on the 3 was pretty bad due to the large C pillar and narrow rear windows.
Overall the 3 is a great car but not quite the ride or quality of the Golf.
Your best bet is to try them, take each one for a test drive, some dealers will let you take the car overnight, this is handy to get more feel for each car.
Go for the car which suits you best after testing and good luck.