Is it possible for me to attack someone with more power than me and still manage to win the siege?

Yes you can. Having more troops will give you more power but the skills of your heroes will often give you an edge. Having 3 hero slots unlocked, having orange heroes and having their skill unlocked and upgraded will make you much stronger than having better troops.

Research for the troop types and some buildings also give you buffs to your APCs so you can be even stronger.