Do you already know how to make a comparison using ほう and より in Japanese? If not, please learn it first.
The sentence in question is an extension of this. While there is no explicit comparison target marked with ～より, this ほう still means "comparatively" or "relatively".
これでも用心深いほうなんでね。
Despite my appearance, (if one has to categorize me either as a cautious or as a careless person,) I'm comparatively a cautious person, you know.
I'm a more cautious person than I may look, you know.
これでも (literally "even with this") is a set phrase, "although you may think otherwise" or "although I may not look like it".
Similar examples:
- このケーキは甘いほうだ。 This cake is relatively sweet.
- 私はよく寝るほうです。 I'm relatively a good sleeper.
- あまりテレビは見ないほうです。 I'm not a kind of person who watchwatches TV often.
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