Personally, given your choice of lenses, I would definitely (and emphatically!) continue to use the 105mm - you'll get way better results with the better of the two lenses.
Secondly, use a tripod as this will allow you to get away with a much slower shutter speed - I often use down to 1/30 but resting on a tripod to minimise shake (and this is usually with longer focal lengths). OK, some shots will fail through the subject moving but it's surprising how still wildlife often can be!
Thirdly, try to increase your DOF to F5.6 or F/8 - you'll get more in focus and that aperture will give even better results from that lens. You'll probably have to up the ISO to 400 or so.
Flash can improve things but I tend to avoid if possible, occasionally using to provide some fill light
Here's a shot from my Sigma 105mm:

7D, Sigma 105, F/2.8, 1/250, handheld
OK, to get this I used a 300mm but shutter was 1/25 and aperture F/5.6 - but tripoded
This with a 70-200 @ 175, F/5.6, 1/400 (should've slowed the shutter as ISO400 - downside to shooting with sun in/out of cloud!), tripoded