If the legion seeker squads were the public invention of the Alpha Legion during the Great Crusade, then the Headhunter kill teams were its more secretive refinement taken to the next level up! For the Alpha Legion, they provide an excellent alternative to the seeker squad (if one was needed), but they pay for it in terms of the sheer points cost of this unit.
I feel that the main strengths of the unit are in the anti-infantry role. Indeed, with preferred enemy against all infantry, this is almost going to ensure that they're going to carry out said role very well indeed. In some respects, they're probably overkill if I'm perfectly honest.
At range, they are capable of dishing out bane strike rounds at BS5 - this is highly effective when combined with their natural infiltration skill. I'd suggest even taking scouts here as the legion's mutable tactics to allow for additional movement to make up for the changed range of the bane strike rounds of the bolters that they carry. This firepower can be complemented with some suspensor aided heavy bolters or combi-weapons. Note they also have precision shot as well (as per the FAQ).
In melee, they're not shabby either. Each member comes with a power dagger as standard. Hence, even if they're striking at S3, they're still going at initiative and will have enough attacks to roll a couple of serious wounds against power armour opponents (but not terminators - take note!). This is aided with the venom spheres that provide hammer of wrath to the unit.
Hence, they're going to whittle down any enemy space marine troop squads very quickly indeed. And this is where their strength truly lies. Keep them away from big tanks and terminators - such things are not their targets.
Fundamentally, they're still space marines with T4 and a 3+ save. Hence they're just as vulnerable as other space marines if they're not paid much attention to. Vindicator shells are going to wipe out entire squads potentially. Plasma guns massed against them will destroy them. And so forth.
On top of this, they're not really that fast -- for a fast attack choice. The only way to make them fast is to use infiltration in combination with scouts. As part of a bigger army that is built around infiltration or scouts (e.g., with lots of bikes), I think they could certainly perform well enough. Or if given a drop pod (they can take rhinos or dread claws as standard). Hence, I thoroughly recommend a dreadclaw drop pod if the army is not taking scouts as the mutable tactic.
Here are a few builds to think about. Remember that I haven't included drop pods or rhinos here.
5 Headhunters, 1 heavy bolter with bane strike ammo (185 points)
This is a "light" version of the squad that focuses on firepower. Although not bad at close combat, they're much better at shooting and that should be taken advantage of.
10 Headhunters, headhunter prime with artificer armour, melta bombs, and power fist (335 points)
Destroy squads of space marines at close range, or in melee. Whichever you like really. Consider double power fists on the headhunter prime if you like as well!
8 Headhunters, each with combi-weapons and bane strike rounds, 1 heavy bolter, headhunter prime with artificer armour, melta bombs and power fist (325 points)
Similar points to the previous build, but a few less members. Shoot every space marine enemy you can. Give the squad a rhino or drop pod, and team up with a HQ for extra fun.
A good addition that is very characterful for the Alpha Legion. That said, they are expensive and I wonder if a terminator squad might be more desirable for the points cost.