Attack or wait?

[The Mouth]

So I'm currently playing a Shogun 2 campaign on normal (With DarthMod). As the Hattori clan I've already claimed the Shogunate, have 21 provinces, and the year is 1567. Some (Semi pointless ) backstory: After claiming the Shogunate, the Realm Divide hit in which me and my allies (The Matsuda, Mori, and Tokugawa) entered a war with the rest of Japan (Shimazu, Satomi, Satake, Takeda, Honma, Ikko Ikki, Sagara, Chosokabe, and Hojo clans). I immediately sent my godly Daimyo with a full stack (With another full stack led by one of his sons and a brother to make war on western Japan) of war hardened veterans to Shikoku. I quickly captured Awaji and Awa and once those were taken I found out what had been preventing the Mori from capturing Shikoku: Two full stacks with 13000 men in total. In an epic siege battle my army of 3000 men utterly crushed our attackers, reducing their force to a mere 1000 men. This allowed me to easily steam roll the rest of the island until I laid siege to Tosa (A stronghold) and I'm faced with a bit of a dilemma, to attack or wait for the defenders to attack me on the field.

My forces:

Hattori Taketoshi 5 Exp

4 Naginata Samurai 3 Exp

1 Naginata Samurai 2 Exp

1 Naginata Samurai 5 Exp

5 Katana Samurai 2 Exp

1 Katana Samurai 1 Exp

1 Katana Samurai 3 Exp

3 Bow Samurai 2 Exp

Enemy Forces: (None are above 3 Exp)

3 Generals

3 Light Cavalry

3 Bow Samurai

5 Ashigaru

3 Bow Ashigaru

1 Samurai Retainers

1 Yari Samurai

I can envision myself taking large losses either way (From the Cavalry and Archers), losses I would rather not have as I would like to immediately press on to Kyushu if possible.

So which shall I choose my advisers? The open field battle where I shall have to face the full power of their cavalry (And still face the archers though they won't be quite as effective) or the siege battle where I shall have to advance under a hail of arrows?

EDIT: Something I forgot to mention, some of my units are at half strength and almost all of them have suffered losses

[Winterspawn]

I think you should wait. Their numbers equal yours, they have lots of bows, and your army isn't at full strenght. Waiting is always the best option if you doubt if you can win, a head on assault on a castle should only be undertaken if you have superior soldiers or very superior numbers if that isn't the case. It is probarly possible to win a siege in that situation, but if that even happens, your army will be so battered you will have to wait forever before you can press the attack again. So...... waiting it is.