Well, first off, I'm assuming that you are talking about ARC Troopers, (ARCT) from Star Wars Clone Wars. If so, and this is me not knowing much about Spartan IV's, these are the outcomes I see.
First off, with the current tech of Clone War ARCT, compared to Spartans, (any Spartan), it would seem that the Spartan tech is more advanced, considering the AI, if any of them have one. Now the augmentations are an obvious factor that gives the Spartan IV's the upper hand in this fight. But putting that against the Clones adaptability, then they will be a contender to deal with. Plus they have a sniper available to them, so that will be a problem. And lets just assume, for this argument, that neither side has any grenades.
Now, considering that they are ARCT, (In my mind, that's the Star Wars Clone Wars equivalent of a Spartan.), then that also gives them an advantage because they are good at what they do. If it weren't for the armor, augmentations, and tech, then they would probably be equally matched, and equally stubborn.
That and they have lasers, going up against bullets. Now I don't know if the Clone armor is bullet proof, because it isn't laser proof, as we have seen watching the show. But lets assume that it isn't and only bullet resistant, like current armor is. Cause I know for a fact that Spartan armor isn't laser proof either.
Spartans have agility, strength, and intellect going for them. While ARCT have intellect, adaptability, and skill. Not saying the Spartan IV's don't have adaptability or skill, cause they do, believe me. But I'm just pointing out the Pros that each side has.
With all this in consideration, and my knowledge of past battles with both groups, this is what I think would happen in all settings:
1. Open Grassland.
Now, I think that the ARCT would win this one, for a few reasons. One, from what I can tell, only two groups of Spartans have had any success in open fields, without any trouble that would be enough to put them in a corner. (I won't say which the first group is, because of spoilers, but the other group is the Spartan II's). Now as far as I know, Spartan IV's aren't good in open terrain. And ARCT, clones in general, have had a pretty good streak when it comes to that. Not saying they win every battle in open fields, but they do pretty good. Plus, taking into account that most of the weapons that the Spartan IV's have, don't have much of long range, while the weapons the ARCT have can make some distance, especially the Long Blaster rifle, which is pretty much a sniper rifle. And it also depends on how big the field is too.
Now, if it were tall grass, then the Spartan IV's would probably be evenly matched with the ARCT, if not, win. That is, if none of them have any grenades.
2. Jungle
Now, for this one, I really couldn't tell you which one would win. ARCT would defiantly have the upper hand because, again, they have a stinking sniper. But if the Spartan IV's have SPI armor, they can camouflage themselves and get pretty close without detection, besides motion scanners. Now, both sides have pretty good reps when it comes to jungle fights, or places with lots of cover, so it would be difficult to tell you which side would come out on top in this one. But I can say that if it were Spartan II's, even without Master Chief, hands down they would win. I mean, have you sees/read their fights in places like Jungles and Forests?
3. Abandoned space station.
Now, with this one, you were really specific General B.H. It has narrow hallways and lots of cover. But there is one factor that I'm not clear on. Is the artificial gravity working? If not, then neither side would have much of an advantage over the other, because neither side have lots, if any, training in zero G's. Spartans would prefer to be on the ground then in the air or space. ARCT aren't like normal clones, but let's be honest, the only one I think I have ever seen actually fight in zero G's is Captain Rex of the 501 company. And he fired off one shot.
Now if artificial gravity worked, considering the factor that ARCT have experience, fighting in ships in space, and that I have no knowledge of Spartan IV's fighting record in Ships in Space, but knowing their ability to fight with cover,
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To be honest, I'm not really sure. To many factors to account for.
I would have to say the Spartan IV's because, once again, dependent on what armor they have, if its the SPI armor, then they have an advantage of stealth. They are also fast. Plus their weapons are perfect for close quarters combat. Then again, so do the ARCT, with their duel pistols, short blaster rifles, and the Chain gun would be a problem. And they have interchangeable armor to help adapt to their situations and surroundings.
For the Spartan IV's, pretty much all their weapons are made for close quarter combat.
So in this situation, now that I have gone through it--
If the gravity was on, then the Spartans would win.
Off, I think it would be a tie.
Now, I based all of this off of my opinion. COMPLETELY MY OPINION!!!!!!!
Also what I know about natural physics, and what I know about terrain, abilities of both sides, and probability based on those abilities. I could be missing a few things in both categories of terrain and abilities, so if I am, please let me know.
And General B.H., if you have any specifics you want me to consider, then please let me know so I can adjust my theories.