The .303 will work on Caribou, or any other North American big game. The trick is as always shot placement.
The .303's biggest drawback is that when compared to other "modern" cartridges, it has a severe trajectory. This doesn't mean it can't reach out, it just means that if you intend to make shots out to 300 metres, don't zero for 50. Shoot at any ranges you intend to hunt at, so you know where the bullet will impact at those ranges. More importantly, know where the bullet is going to be in the intermediate ranges. For instance, if you have a 200 metre zero, you're rounds will hit point blank around 30 metres away, then about 4 inches high at 100 metres, and about 8 inches low at 300.
The most important factor in taking longer range shots is having a gun that is capable of shooting that far. A caribou's vital zone is a bit bigger than a volleyball. If your gun can't group every shot inside a target that size at the range you intend to hunt, then you're asking to make a bad shot. I like to practise with paper plates for targets.
Anyways, a little off topic, but I hope this helps.
Cheers.
Tim