I don't see any big difference between A1200 and A2200 other than battery type and viewfinder in paper.
+ A1200 has viewfinder and uses AA batteries. (Since your budget is tight confirm with the dealer that you are getting charger and rechargeable batteries along with the camera, else you have to spend some more to buy them)
- If you are getting charger in the bundle, it will be basic mini charger charger. It takes long time to charge the batteries, say 12hrs while Li-on charger (A2200 uses Li-on) will charge battery in 2-3hrs.
- Both the cameras don't have IS. It's one of the major drawback. But in this price range and feature filled camera you can't ask more.
- Performance is very slow in A1200, don't know about A2200.
As far as battery life is concerned, Canon claims A1200 shoot 200 shots using Alkaline and 450 shots using NiMH while A2200 (Li-on) shoot 280 snaps. If you turn of the LCD and use viewfinder, probably you will get 1000+ snaps using NiMH (A1200).
And how long a pair of NiMH batteries last shooting video???
It's just my guess. A1200 shoots approx 20% more snaps than my cam. So it should shoot 20% longer than mine which is about 85minutes (mine is 70 min). If you can use viewfinder to shoot videos, you may get longer battery life. While A2200 should shoot video for around 60 minutes may be more.
I don't see any huge + on A2200 in paper. It may score in performance, I am not sure. Those who are using or know about these cameras may comment...
You are gonna buy it from local dealer, right? You check these cameras image quality when buying. Take few snaps and check it.
Check these two models too...
Olympus VG120 (Wider lens and more zoom)
Panasonic S1 (This model has IS, but aperture is not as wide as Canon and smaller sensor)
Check image comparison of A1200 vs S1 here
Product Face-Offs Digital Cameras : Fujifilm FinePix X10, Lenovo ThinkPad Tablet, Pentax , Samsung NX200, - DigitalVersus
Compare the specification of all the four models here...
Side by Side Comparison: Digital Photography Review
Panasonic LS5 seems to be good as well... Check that too...