1. Probably sturdier
2. Easier to get in there to access stuff

On the other hand, the stuff sack approach has

1. Waterproof, assuming it's a dry sack
2. Cheaper
3. Lighter

Personally I'd just use the stuff sack and not put anything in there that I'll need to take out during the day's riding. Then you can get the mini pump - a Topeak Road Morph or Mountain Morph is perfect.