Strictly speaking, his view differs somewhat from mine.

Literal

Strictly speak-[if-と], his [possessive-の] view [topic-は] mine [from-とは] somewhat differs.

綿密に言うと ('strictly/precisely speaking,' lit. 'if one speaks in detail') is a conjunctive frame for hedging with precision. 綿密 ('detailed, thorough') — note the kanji 綿 ('cotton'), used metaphorically for 'dense, close-knit.' 私のとは ('from mine') abbreviates 私のもの to 私の, a common short form where the referent is clear from context. いくらか ('somewhat, to some extent') is a soft hedge.