Present tense can convey a sense of immediacy that you might want for short introspective pieces. But for longer stories, particularly those involving multiple characters, present tense can become awkward, requiring over-use of the verb "is": Foreman is scowling, Cameron is moralizing, Chase is hiding, etc.
A combination is possible, but only under carefully controlled circumstances. In my House/Holmes story, I've been using past tense for the regular narration, but switching to present tense for the flashbacks. So far, nobody has complained that this technique is annoying . . .