Hi
I am an INTP straight female w/ some pretty strong opinions about an INTP-ENTJ match up (generally I LOVE them! although I'd really like to try a relationship w/ an INTJ to compare).
I find romantic match-ups with ENTJs to be thrilling, exciting, full of energy, and dangerous (explosively so). ENTJs always want to know what I'm thinking (can't ever guess), and I freely tell them when asked - and they usually get a kick out of my answers because whatever I'm thinking is likely smart, logical, and objective (99% of the time). I think ENTJs get annoyed with stupid people, and it's a change of pace for them to know an INTP. Also, the INTP will concede a point easily if you prove it to them, and the ENTJ loves that the INTP will genuinely concede a point (by genuine, I mean we'll concede w/ no strings attached; I think other types resist the ENTJ's logic on principle b/c ENTJ's are often jerks about being right or appear to be jerks about being right - but the INTP doesn't care if you're a jerk as long as you're right; we won't harbor a grudge b/c you were right and we were wrong, as long as you show you're right). But beware, just b/c an INTP concedes point "A" doesn't mean they'll follow you from point A to B to C to whatever conclusion YOU WANT w/out questioning all the logical steps: INTPs will call you out whenever you've failed to prove something to them and they think your conclusion is off.
ENTJs are controlling but not in a way that bothers me. I know MB says INTPs don't like to be controlled, but because the ENTJ is usually SO OBVIOUS and logical about it, its not problematic (I think INTPs just don't like to be secretly controlled or manipulated or slowly backed into a corner; we HATE being controlled by feelers, but thinkers aren't so bad). Further, the ENTJ is likely to be so opinionated that it takes the drama out of the decision-making process the INTP. The INTP can just say "yes" or "no" to the ENTJ and that's the end of it (of course, it's important in this that the INTP thinks the ENTJ has a brain, but assuming the ENTJ does, the INTP is probably willing to follow the ENTJ overall, even if the INTP questions a few decisions here and there).
But, there's a major, major pitfall in everything I've said, and I think it's the possibility of stalemate or all-out-war regarding the actual relationship itself. The ENTJ is used to being able to push people around, and you can't push an INTP around WHEN YOU'RE NOT RIGHT. In such a situation, the ENTJ will often take a "my way or the highway" approach. When all else fails, i think ENTJs are used to pushing their agenda whether or not they're right, but, surprise! the INTP will tell you where to shove it if you're aggressive + wrong. The whole time the INTP was w/ you b/c you're smart and logical (your domineering antics never really worked on us even if you thought they did). SO, if you're a jerk w/out being right, watch out. You may have been bluffing, but if you were wrong, can't admit it, and bluff aggression/assertiveness, the INTP will walk (having given you a chance to admit you were wrong, that you didn't take, WE WILL WALK w/out ever looking back - seriously, that's it: finito, finale, end).
The only other worry is that the E/I mis-match will leave me wondering if you're board with me. I need an "e" that can have outlets outside the relationship for their extroversion w/out physically or mentally cheating on me. I need to trust the ENTJ to get what they can from me, responsibly get other needs met by other people (we're not jealous at all, so it's up to you to be a responsible romantic partner), and NEVER make me feel boring. An INTP can be one of the few people an ENTJ can let their guard down around; You can be alone with your INTP, so appreciate them for that and don't expect them to be loud and crazy w/ you all the time.