Things that could be factors:
- Genuine flaws in the bike. For example, I had a new bike where there was something defective with the headset. The symptom was that if you held the front wheel in place you could still turn the handlebars without the front wheel turning. The bike shop was appalled and that's very dangerous and fixed it for free by replacing the stem.
- Poor bike fit. Perhaps the new bike is a little to big or small for you so it's not as natural to control.
- Tires. The fatter the tire the more junk on the road it can roll over without a problem. The drawback is that fatter tires are generally slower on pavement. Also really cheap low quality tires can more easily lose grip on the road especially if the road is raining.
- Clipless. If you need to get a foot down in an emergency clipless will slow you down a little. For most people it's not a problem, but for a few people their brain and muscle memory never quite "get" it and they'd be much safer with flat pedals. If you struggle to unclip from clipless and you face serious dehabilitating injury if you fall over on the bike you should definitely go with flats.
- Pedals. Cheap slipper pedals often come with bikes and people have issues with their foot slipping off the pedal, you can get much better pedals for the bike. For example the Shimano PD-GR500's are $50 and a good quality pedal with a good shape and metal pins. If you really want absolute traction on the pedal you can also get five ten freerider shoes which use a special extra grippy rubber that will not slip off the pedal without lifiting your foot up.
- Riding position. Some bikes definitely have you more hunched over than others. However, the specialized sirrus is a fairly upright bike (though there are more upright bikes with better visibility for riding).

But the biggest factor is crashes is your awareness of the vehicles around you and avoiding ever being to close to them. Is is odd that you keep getting brushed by bikes or cars. Ever since someone I know had a crash when a jogger on the trail turned around without warning right into them, I make sure to leave at least a person worth of space between myself and anyone I'm going around or by.