Well in this scenario the answer is obviously the Spartan 3s.
There seems to be this big misconception about the 3rd Generation Spartans, so many people think that they are inferior to Spartan 2s.
Lets analyse this issue a little more before I explain my answer to this topic.
Spartan 2s were kidnapped children what were screened for very strict genetic parameters.
-“who were selected by a gene-candidate pool, and must fit into a certain age restriction protocol. They must also have possessed superior physical and mental attributes.” (Dr. Halsey’s Personal Journal)
Spartan 3s were ‘volunteers’ that were screened from a wider genetic pool that the Spartan 2s (though the general genetic profile was the same)
(Note: The genetic profile was needed to increase the rate of survival for the augmentation procedure. They did not magnify the effects of the augmentations themselves; it was the synergy of all augmentations acting together that did. -“The results of the augmentations on the successful candidates were unprecedented; the SPARTAN-IIs performed well beyond the projected capabilities. Dr. Halsey suspected this to be due to inexplicable, synergistic effects resulting from all the augmentations acting in concert.” (Halo Fall of Reach).
So this means that Spartan 2s were selected from the best of the best Humanity had to offer. While the Spartan 3 screening was less strict we know for a fact that some members had the genetic requirements of the Spartan 2s (Cat 2 Spartan 3s ie: Noble team for example)
For the augmentations Spartan 2s were given:
-Occipital Capillary Reversal
-Carbide Ceramic Ossification
-Catalytic Thyroid Implant
-Muscular Enhancement Injections
-Superconducting Fibrification of Neural Dendrites
Extra information: “The process of augmenting the SPARTAN-IIs was divided into two parts, surgical procedures and injection procedures. Surgeries were highly risky, intensive, and required special medical talent. Their safety and effects varied substantially from subject to subject, with the benefits and risks varying with the surgeon, the surgical conditions, and the state of the patient. Chemical augmentations have their own risks dependent upon the subject’s genetic background and how they adjust to the alteration of cells and molecules and to a more physical point, tissue growth. SPARTAN-IIs also underwent extensive gene therapy” (Halo Fall of Reach)
For Spartan 3s:
-carbide ceramic ossification catalyst" drug
-fibroid muscular protein complex" drug
-retina-inversion stabilizer" drug
-improved colloidal neural disunification solution" drug
In addition to their chemically-administered primary augmentations, Spartan-IIIs were subjected to a number of surgical alterations to enhance their capabilities.[9] Their circulatory systems were also augmented from the human baseline.
Gamma company also received:
-Neural-altering non-carcinogenic mutagen + 2 drugs to counter the negative effect of this drug
Extra Information: “The CHRYSANTHEMUM bioaugmentation set improved upon the augmentations of the SPARTAN-II program. With advances in technology, the casualty rate for Spartan-III candidates was usually 0%, as opposed to the 56% casualty rate of the Spartan-IIs. Most of the Spartan-IIIs’ augmentations were chemically induced instead of surgically implanted like many of the Spartan-II enhancements.The genetic requirements for the Spartan-III candidates were loosened from the exceedingly strict criteria of the SPARTAN-II program, although the range of compatible individuals still remained incredibly narrow, with any aberrations from the required genetic set geometrically increasing the failure rate”
(Note: These hormonal treatments supposedly replaced the catalytic thyroid implants received by the Spartan-IIs as part of their augmentation procedures. When describing the CHRYSANTHEMUM augmentations, Halo: Ghosts of Onyx does not mention the Spartan-IIIs receiving the growth hormone catalyst in the form of a thyroid implant like the Spartan-IIs. Since the Spartan-IIIs received human growth hormone months prior to receiving their augmentations, it can be inferred that the catalytic thyroid implant was rendered redundant since both serve the same purpose. )
So when we use all this data and combine it with known feats of Spartan 3s it can be inferred that Spartan 3s are physically equal or slightly weaker than Spartan 2s (except for gammas which are stronger and tougher)
As for training:
-Spartan 2s: Began September 24th 2517 and ended September 11th 2525 (so roughly 8 years of the toughest training at the time)
-Spartan 3 alpha: Began December 27th 2531 and ended in November 2536 (so roughly 5 years of tougher training than Spartan 2s)
-Spartan 3 beta: Began sometime in 2539 and ended sometime before 2545 (so roughly 6 years of tougher training than Alpha company)
-Spartan 3 gamma: Began sometime after 2544 and ended in October 2552 (so roughly 8 years of training that made them “the finest Spartans ever”)
(Note: Spartan 3 training also included analysis of Spartan 2 tactics)
(Note 2: Spartans of alpha and gamma had a Spartan 2 to train them and gamma had two Spartan 3 beta on top of that)
All this information put together leads me to believe that (on average) Spartan 3s of alpha were slightly lesser than Spartan 2s, Spartan 3s of beta were equivalent to Spartan 2, and that Spartan 3s of gamma were better than Spartan 2s (at the same age)
One more thing before I analyse the scenario.
People think that Spartan 3s are a lot smaller than Spartan 2s. This isn’t true. On AVERAGE Spartan 3s are SLIGHTLY shorter than Spartan 2s. But just like some Spartan 4s, some Spartans are of similar height to Spartan 2s (ie: Tom-B292)
Finally the scenario:
Spartan 2s: haven’t quite finished honing their capabilities, no MJOLNIR, only 3 of them
Spartan 3s: (as they are already equipped I am going to assume their training is complete at the very least), SPI armour (which does enhance the user, just not as much as MJOLNIR), they are 10, and they have weapons.
… Yeah, I think i’ll be betting on the Spartan 3s thank you very much.
The Spartan 2 are definitely the real deal, however in this scenario they have WAY too much stacked up against them. It doesn’t even matter from which company the Spartan 3s are from, nor even if they are CAT2s or not.
Sorry about the essay level response. 
Have a nice day!