They have a very special module, that might have been made specifically for heavies, it's so perfect for them.
CCP noticed that heavies were horribly, horribly, slow, and so they gave us... the LAV.

What makes it even better than a regular speed boost, is that it even helps you heal when you use it.
It's just like extra armor. oh wait, it IS extra armor :-}

Minmatar sentinel is 6.7 sprint speed with one complex, 7.44 with two

As for gallente vs minmatar...yes the gallente has an armor repair bonus, but the faster shield recharge, and more shields on the minmatar is better suited for speed as the gallente will be good in the first encounter, but get screwed over in the second.

The thing is, the minmatar doesn't have the option to completely speed tank. If you do that, you're wasting 550 armor that would be more use to you if you could repair it back.

However, minmatar regens stamina like CRAZY, so while you might not move faster than a gallente with 3 sprint mods, you can recharge your stamina faster and sprint whenever you want instead of having to walk around slowly aiting for it to recharge.
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Now for the HMG

You're looking at a weapon that practically immobilizes you when you fire. Because you can't sprint and fire your movement speed is what you're relying on, and the minmatar again wins in this category.

However, going up against other HMGs will be difficult, as the winner of an HMG duel is who fires first, who gets the most headshots, who can deal the most damage, and who has the most health.

Pretty much what that means is that the minmatar suit CANNOT go face to face with other heavies and survive easily. UNLESS you use the burst HMG.

Why the burst? Well unlike the standard one, you can deal an insane amount of DPS with one burst (we're talking enough to instantly kill std or advanced suits, or a proto if you can land a headshot).That's not the main benefit though...

The burst HMG allows you to move around while you're fighting. Burst, sprint jump, burst, hide around corner, pop out, burst, run away...

It's very similar to a shotgun because of this, and works well as a counter against scouts too. However, keep in mind that the burst is only good in 1v1 matchups. Unless you are really good with it, taking on more than one enemy will be suicide. As long as you stick to engaging one enemy at a time, the burst will do all the work for you, and absolutely melt other heavies that you will no doubt have trouble with.

Matar Sent.

Someone posted above about the basic heavy frame being better for speed tanking...Since the minmatar skills are **** anyways you don't even have to skill into minmatar sentinel to try it out, AND it's faster (I'm actually going to make a video about this, because I didn't even know about it lol)

The gallente sentinel actually has some decent bonuses though (dual armor resistances)
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I usually run one sprint mod and one armor repair in my lows. While you can get a much higher armor repair on the gallene, you're losing out on speed.

A gallente with 1 sprint mod is 6.3 or 6.4 sprint. This is not fast enough, so you'll need at least 2 to compare to the minmatar. Now you're running at about 6.7 or 6.8 (I could be wrong here).

At advanced you have one more low slot, allowing you to have 7.25 armor repair vs 6.25 armor repair on the minmatar sentinel.

EHP is about 1200 on gallente suit, 1050 on minmatar. So at advanced the gallente is slightly better in terms of speed and armor, but the minmatar is better at bringing back your shield buffer, increasing the effectiveness of the shields itself (two high slots can give you 550 shield with 30 shield regen), and moving around. You could even put damage mods in those two high slots but I wouldn't recommend it with the burst
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If I were you I'd choose based on how much sp you're going to be putting into it.

At proto the gallente sentinel has a HUGE advantage over the minmatar. You can speed OR armor tank the thing, you get really good bonuses, and you can stack armor repairs and sprint mods for a devastating speed heavy.

Proto minmatar doesn't really give you anything. You get a high slot for better shields (or a damage mod on top of your shield modules), but you're still limited to two low slots.

Here's a video of the minmatar heavy in action (the second half has burst HMG footage)
https://youtu.be/w5FonW5CH7E
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My preference is the Minmatar only because of the shields. I've been playing heavy for a long time now and relying on your armor is not very effective from my experience. I do prefer armor over shields, but when it comes to speed, you want as much ehp as possible before you engage the next enemy, and the ability to get it back fast. While the gallente is more effective, it has a longer downtime between enemy encounters.

Marginally. 390/425 base before Upgrades, iIrc. Pop on an Extender or two and it's pretty much even, depending on which tier you use. Keep in mind that Gal's built-in rep is only 1 hp/s with 525 base armor before Armor Upgrades. It's gonna take a lonnnnnnnnnnnng time for that be of much use unless you're running proto and throwing on complex reppers. You pretty much need a logi no matter what.

Min also has .2 m/s higher base movement speed, which is surprisingly useful when you slow down to engage and strafe.

I think you may be a BOLD CAP freak as well

Gal sent....4 complex kin kats...for sprint of at least 7.81

You're asking for a hybrid speed/stealth/attack heavy? Such a combination does not really exist. You can get one of any three, possibly two of them with lesser preferences, but all 3 is just nonsense.
You'll need at least 2 dampeners for casual "hiding" and 3 catalyzers or so to "Run", also one low slot for a repair or energized armor.
That's about 6 slots predetermined... if you can even fit that many slots.

Update: Gallente Sentinel
3 Complex Kinetic Catalyzers
1 Enhanced Cardiac Regulator

7.85 Sprint
4.25 Movement

~475/675 Shields/Armor

I outrun everybody. Scouts without any Plates are the only ones to get by me.
When I get my aim dialed back in, you will hear "Nerf KinCatz on Heavies" on these forums.