The hellbore has special armor-removal mechanics and is functionally a torpedo. It takes advantage of an opening to do damage.
The HAG is constant pressure with anti-armor focus. It dictates the defensive stance of your opponent.
I don't think the Hellbore has any special armour-removal mechanics, it just has high hit strength, which determines damage to armour. Nothing crazy going on there!
What that means is if you are unloading on a ship with a HAG, it wants to keep it's shield up for the duration of the barrage because it will be punished if it doesn't. This shifts the focus much more heavily into flux management over pure tanking. It also allows you to force a choice between two bad decisions...
...HAGs on a flux efficient build are great lineholders and will push back very strong ships until you are ready to deal with them.
I agree on the HAG keeping enemy shields up (it is a lot like the High Intensity Laser in that regard). Not sure that Sabots make for a great example, because as you mention, the enemy can drop their shields and eat the (since update, relatively minor) EMP damage and a couple HAG rounds. That, or employ point defense, which is really quite cheap flux-wise. The Squall example is better, because both the HAG and the Squall are able to fire for extended periods, so the enemy can't flicker the shield on or off for burst damage.
Not sure I agree that HAGs are "great lineholders". Ships are great lineholders. HAGs are just guns. Flux-heavy guns, at that. There are few ships that have the flux to even use an HAG effectively, let alone use it with other kinetic weapons at the same time! Without those kinetic weapons, the HAG is really quite weak against even light cruiser shields, so they don't really drive up flux fast enough on their own to push enemy ships back.
A couple decent paring of weapons are Sabots for the "two bad choices" shield-slap, and Breach SRMs. Breach SRMs are super tanky high ammo-count missiles that the enemy wants to take on the shields if you are trying to flux them out with shield pressure, and have the side benefit of special armor-stripping for more HAG damage if they drop, or dont have, shields for any reason.
A side benefit of the rapid fire is the incidental hits against missiles and strikecraft (and frigates) that get between you and your target giving you flux-free "point defense".
Breaches are nice, but if you have an HAG then you probably want to focus more on other missiles like Sabots or Reapers, Proximity Charge Launchers, Atropos, something that just does a lot of damage, to help with shields. The HAG should be all you need

The hellbore can make an opening hurt badly. Any time you would sling a reaper you could instead use your infinite hellbore ammo to do similar damage. While the HAG can arguably be used in these situations, it is less focused and doesnt have extra armor-shredding. Removing armor is niche but it has it's uses. Fragmentation damage tends to be very high DPS, but does 25% damage against any defense. If you can make an opening for them with a Hellbore, you can do incredible DPS to a large ship/station. Reduced armor also simply takes more damage from any other things you have hitting it. Strikecraft (fighters/bombers) like to use Fragmentation weapons or light anti-armor weapons. If you have carrier support, or are a carrier with a hellbore, you can remove the armor to make the cheaper strike craft far more effective.
Hmm, not sure I understand your point here? Fragmentation damage will be just as effective whether the armour was stripped by Hellbore or HAG? I feel like, aside from stations and lumbering heavy-armour ships in particular, an HAG would result in more damage simply because of the sheer hull DPS the HAG boasts.