Mind/ on dominators all about control, but does not do much direct damage. Confusion bypasses this by letting enemies 'help,' but it is at its core all about enemy manipulation rather than enemy defeats. It has 4 1/2 AoE controls to cycle through, 2 of which are readily available but 'breakable.' It also has 3 aggro-less powers, making it very good at enemy pre-mez before a fight. Its single target controls are fast and diverse, allowing a one-hit boss sleep, a fast hold, a fast boss KU, a long-lasting confuse. If something resists one effect, you can use another.
Fire/ is a hybrid, helping kill things faster but by doing so, it trades a lot of control. It has only one fast standby AoE mez, (flashfire) and its backup AoE is the close-range hold. It only has one single target 'stop attacking!' power. So for actual lockdown powers, you will only have 3. In addition, you get a kb patch for area denial if you wish, a -perception to reduce outside mob additions (less reliable than a sleep) and two flavors of immobilize. It's actually pretty scant on control, to be honest. But when you have a massive fiery aura boosted by embrace of fire, a trio of happy burning imps slashing at your foes, and orange numbers pouring about, you'll 'get' it. This is not the set to stand back and observe your helpless foes. You are in a race to destroy your enemies before they can rouse themselves and kill you.
With perma-domination, no other archetype in this game can compete with the level of control Mind/ can bring. Permanently sleep archvillains. Hold them. Confuse them. But you'll still not be killing things that much faster. You'll just be living longer, if not indefinitely. (Depending on how alert/well timed you are.) Fire/ on the other hand gets to use flashfire a lot more often, for longer durations. As such, your race for survival will be a lot more one-sided to your favor. You won't be able to face against big enemies as well as Mind/, but your flashfire being stronger and faster means you can pick up the pace wasting mobs.
Overall I agree with Seldom's writeup, so I'll focus on something else. 
For me pets were a big factor. I have a Fire controller and occasionally the imps will aggro a spawn when you didn't want to. For Mind, your "pets" are really the NPC enemies you're facing, but one benefit is no matter who they attack, it doesn't lead to aggro on your team. Obviously that's only one factor among many, but for me it was significant.
Freedom: Blazing Larb, Fiery Fulcrum, Sardan Reborn, Arctic-Frenzy, Wasabi Sam, Mr Smashtastic.
Thanks, very helpful. My playstyle prefers frenetic to methodical, so Fire is probably the best choice for me.
Fire/Fire is a very fun combo. The kind of thing that lets you set so very much stuff on fire that you can't help but cackle with glee. But some things to keep in mind; immobilizes come early, but should be used late in your character. They are dangerous to you, and will grab more attention than you can often cope with. Flashfire is what makes the Aoe immobilize useful- stunned foes wander, so flashfire+fire cages=a hold.
Flashfire will often be the only thing to keep you alive, especially against larger groups. Take it ASAP, slot it to the gills.
Play smart, burn what you can kill fast, lock what you can't. You will be very squishy for a while, but after 38 when you have lots of slots, good enhancement value, and all your big attacks you will feel the power in full...and that's before you get ancillary/patron pools to boost your AoE/damage/survival even more.
Fire/fire is a squishy, powerful aggro magnet. It's best when you know just how much flack you and your enemies can take, and can time/position your powers for maximum effect. Because there is very little margin of error between you standing over them in triumph, and you waving hello as you pass the hospital nurse. Candy, target choices, and power order decisions all come into play. And the early frustrations with a still developing character, combat missteps, and the intimacy with the various flavors of flooring make the combo all the more enjoyable once you gain the upperhand, and the play becomes natural and fast. It's very satisfying and fun.
What are the differences going to be between these two? More dam, more hospital trips for fire, better control 1-50 for Mind? Is Mind significantly better at lower levels? I know Mind has the whole solo AV thing going for it, but I don't really care about that. Can they both solo normal content at roughly the same xp rate? I'm pretty confident they can both be powerful team players. Does Permadom help one more than the other? Thanks!