As other people have mentioned, there is much variation in the pronunciation of reduced vowels in English. In certain dialects, unstressed "/ɪ/" has fairly regularly merged into /ə/. This is called the "weak vowel merger".
However, for speakers without the weak vowel merger, my understanding is that both "competent" and "competition" could have /ɪ/. It seems to me that in accents without the weak vowel merger, the letter "e" tends to represent /ɪ/ in unstressed syllables, except for when it comes before a sonorant consonant like "r" or "l", or sometimes "n". The OED entries for competent and competition, which were first published 1891 and have not yet been fully updated, give the pronunciations as /ˈkɒmpɪtənt/ and /kɒmpɪˈtɪʃən/.
More recently updated OED entries, like the entry for genetic ("/dʒᵻˈnɛtɪk/") use a special symbol /ᵻ/ to represent a reduced vowel that can be pronounced as /ɪ/ or /ə/.