I just did a combat to actually test the above and it certainly is contest of patience as the combat will drag on for a very LOOONG time..
The light forces actually start to get the upper hand relatively early as the moral of the LAV marines start to falter and the damage on the static drop faster and faster due to how moral effect the battle as well.
Starting forces was...
3 Space marine regiments of...
1000 Spacemarine grunts (PWI, Power Armour)
200 Spacemarines Heavies (LAV, Power Armour)
against...
3 Garrison Regiments of..
3000 light Infantry (PWL, Light Armour)
60 Fortifications (HCAP, Heavy Armour, Static)
The cost of both are pretty much the same, the space marines could be a bit cheaper if they used PW instead of PWI but that does not seem likely in most cases to arm them like that so I did not.
After about 2 months of fighting..
Marine Grunts in each regiment are roughly 580, morale is 91
Marine Heavies in each regiment are roughly 43, morale is 70
Light infantry in each regiment 1700, morale is 91
Fortification in each regiment are roughly 45, morale is 90
Losses are now roughly about 1.5:1 so Space Marine looses 10 every 8 hour cycle and the other side about 15 light infantry and very rarely a fortification unit.
The Space Marine side still burn about 2970 GSP while the light infantry side burns 2338 GSP. From the start the Space Marine used up 7350 GSP and the Light Infantry side 3870 GSP.
I presume the fight will go on for a long while and if both side had been max fortification from the start then things would have taken way longer but that was not the test.
Why do I compare like this... because you have to do it this way... there is no point in having one side attack and the other defend... this test is about who is more resilient in defence and that is what we are testing. There are a few key reason why light infantry combine very well with static units which have to do with distribution of size and morale and allot of HP distributed on many difficult to hit units. Another thing is big difference in armour and damage distribution capabilities making the enemy waste as much AP and Damage as possible which cost resources and supplies.
Artillery is also something interesting to discuss... if you build artillery for defence there is almost no reason to put any armour on it as you are always better of with just more of it. But if you are going to assault a planet you should put as much armour on it as possible because that means it will survive better for the space it takes up on the ship. This is important when you look at counter battery fire.
If we are talking about invasions then there is no point in comparing costs as that is not what matters as much as the capacity to cram as much firepower and defensive capability into as tiny a space as possible, that means very costly units in terms of resources. If you instead would compare the marines with the light infantry and static with space on a drop ship things will look very different. You also most often can disregard supplies as you don't need to drop formations with lots of supplies. You can bring most of the supplies with regular troopships and unload it as you need it, more or less, so you are much less restricted in space for support forces.
The three space marine regiments above are about 7500t while the light infantry is over 10.000t worth of troops so not very space efficient, static units are not very good at attacking either so you would need to replace them with a vehicle type instead.
Another important thing to note is that technology difference also play a VERY big role on the importance of armour or numbers. But if all things are equal then numbers wins over quality. If your armour technology is better than their weapon technology then heavily armoured infantry will likely be more effective.