Order Spearmen:

150 men per unit
11 attack
20 defence

730/155 in cost/upkeep

Samogitian Axemen:

120 MPU
16 attack (armour piercing)
14 defence

440/125 in recruitment/upkeep

So far so good. In an equal fight (3v3), the OS are clearly victorious, mainly due to superior numbers. In a 3v4 fight, the axemen are clearly victorious. The OS give ~50% casualties, while the axes give about 30-35%.

However that's not telling the whole story. A staged fight just between these two units, with the numbers always favouring the axes to make the men count equal is not a fair way to analyse the units' power and potential in a forced AR game. First of all, the initial unit training costs are very different - the axes are 40% cheaper. However upkeep is the much greater limiting factor on maximum army size, and that differs by only 20%. I would say that based on gold, it is fair to say that for 10 OS, the enemy will have 13 axes, but not FOR ever 10. The ratio will change based on unit numbers. For a full-stack, the troop numbers will be in favour of the OS (even if you have one or two more units of axes) as upkeep will devour most of what is saved from the initial cost. If the OS have any numerical advantage, they are going to win.

Now, let's factor in some other things. First of all, making pure armies is not practical in a hectic hotseat, unless you can sit back and build elite armies or you control the pace of the game. The fighting in this campaign begins around turn 3.

The TO can recruit spearmen out of any castle with a Tier 2 barracks or greater. They start with four stone castles in their possession and the option to upgrade the barracks structure and armour smith in all of them. The Lithuanians in comparison, can only recruit these axemen out of their temples. They have only one starting city that has the correct temple. So one turn of demolishing and another turn of building is needed before they can be on at least even footing to the TO in terms of production. By the time you get your first wave off, the two TO fullstacks will be knocking on your door with catapults.

Now let's consider other things. The TO has greater starting armies for autoresolve (and arguably for lead-battles as well). They start with at least 10 units of order spearmen and can crank out 10 more on turn 1. They get a mission that grants them free units for the taking of a small village up north, and those units are either Christ Knights or Order Spearmen (50/50).

And that's still not all. In a pure 3v4 situation the spearmen lose to the axes, however in a mixed stack the units with the greater armour give lower losses than the less armoured ones. I observed this multiple times in Britannia with Gallogaich and Armoured Swordsmen mixed together. When fighting mixed armies with mixed armies, your medium armour AP attack troops will pack a serious first punch but you will progressively become weaker as you fight more, since they lack the sustainability of high armour units.

Retraining is a pain, as you will have to build temples in newly conquered regions. It's even worse if you lose settlements, as the game automatically razes religious structures upon conquest, so you will always lose your troop training centres. You can't return the favour however, as the TR rules forbid the razing of structures (such as barracks).

Overall I'd still say the TO and OS win out. Not to mention that you can't survive the onslaught with just 1 unit per turn per training center. You'll be forced to recruit other units, and Lithuania's other units are all weaksauce for AR.

In comparison, the TO can make Sword Bretheren with 15 defence, very strong cavalry units and quite decent pike militia units right at turn 1.