It's always good to ask questions like these. My opinion: a 270 (or any cartridge in that class) is really hard to beat for a deer rifle. But deer are pretty solidly built, and typically shot at 100 yds or so, so people like rifles that shoot flat and hit hard. Rabbits, on the other hand, are pretty fragile. If you shoot a rabbit with a 270, you will need a couple of hours to pick up enough pieces to make a stir-fry. Same story with the 223. If you shoot rabbits with either round, you will understand the term "overkill". Rabbits and other small game are best hunted with a shotgun with small to medium size shot, or a 22LR.
It sounds like you need:
A) a shotgun (covers both small game and deer) OR
B) a 22LR for small game and a deer rifle for deer (270 or other chambering of your choice).