You fight the campaign with three companies. If you get the Fox Co. DLC, you’ll have to choose three from the total of four available: Able Co. (Airborne), Baker Co. (Mechanized), Dog Co. (bog-standard infantry), and Fox Co. (Rangers).
Fox Co.’s Ranger squads are expensive but come with Thompson submachine guns and can be upgraded with bazookas or panzerschrecks as well as other abilities to make them the most powerful unit in the game. The big negative for Fox (though I have not seen this described, let alone quantified, anywhere) is that it accumulates experience much more slowly per kill than the other companies, so if you are aiming for a high campaign score (e.g., >30K) and can realistically achieve it without Fox Co., don’t use that company.
The other three companies have squads that are very weak at the outset of each mission, compared to German units. Un-upgraded airborne squads, for example, will be wiped almost immediately even by sturmpios. In general, all initially available squads, except Fox Co.’s Rangers, cannot fight effectively until they are outfitted with weapons such as BARs and bazookas and supported by HMGs and AT guns. The less experience these companies have, the fewer units they will start with on each mission, so the weaker they will be.
Dog is good for defensive battles, has good AT-artillery, and has amazingly powerful anti-personnel artillery when fully upgraded.
Baker has good halftrack-mounted infantry, which can come with BARs or LMGs, if you can afford to wait until you reach 2 command points, and they have cheap late-game armor support (8 CP) that costs no fuel.
You fight each mission with one company, but you normally will use the other companies to cut off escape routes for the Germans being attacked on that mission. If you don’t do that, some of the Germans who survive the battle will flee to nearby German positions, making the difficulty level higher at those positions. In some circumstances, you might want to deliberately make missions harder so that your experience accumulation will be greater. But difficulty levels 3, 4, and 5 are all very challenging, and on level 5 even an experienced player who always wins can take dozens of casualties doing so.
Due to the limitations of contemporary coding, and maybe of the devs’ competence, the AI is at a significant disadvantage against a human-brained opponent, if all else is equal. So of course, pretty much everything else is unequal. This bias is mainly embodied in the German units and their superior hardiness and weaponry. But there are other “cheats,” the biggest (and least-discussed) one being the unreal visibility limit that is frequently imposed on the human player and prevents his HMGs, AT guns, and other units from auto-firing in the presence of a German unit, even when the German unit can fire at his units. This visibility cheat may be in the form of ordinary “fog of war” or it may be presented as smoke/dust from battle. Be ready for it, in any case.