First, if you are playing vanilla '36.game, there's no logical reason for Belgium fighting Allies, ever. Something really funky must've happened :D
HG:
They're both amazing games in their own ways.
Yes and you can add Victoria to that list, especially now that Revolutions fixed the major issues in old Vicky. EU3 is the first major Paradox game that I didn't get into, the 3D-map turned me off. Good thing that they seem to have improved it for HoI3.
I think artillery is the best choice, but antitank sucks.
Yes, usually artillery > antitank, but it is useful when you need to shore up pure INF-stacks against plenty of Soviet tanks. Late game, US can also wield pretty hefty ARM/MEC-stacks where AT is useful. AI does use Heavy and Super-Heavy Armor.
Engineers are good but that little speed boost just might not be worth the cost, and even with them attacking across a river is usually a bad idea.
Engineers also give defensive bonus unless it's been changed, which helps a bit. The speed bonus is useless. There are situations where you cannot avoid attacking across a river.
Regarding brigades, do remember that you can re-attach and shuffle them around. They do spend couple of days in deployment pool but it can be done. Also, only use for AA-brigades is to put them with HQ-divisions, especially if your playstyle requires lonely HQ's. AI bombers love to concentrate on HQ's so the extra AA is very useful.
Personally I create 3 div Korps(Lt.Gen) and 9 div Armees(Gen) - and then HQ's are alone, with a FM in them. Also, NEVER stack INF and ARM/MEC together under the same general, since the ARM will make the stack stay in-battle longer thanks to its toughness, making the softer INF divisions take a nasty beating.
1 ARM + 2 MOT or 2 ARM + 1 MOT is best for penetrations to get the extra +10% Combined Arms bonus. When you get MEC-troops, you can safely ditch that bonus since by that time your Panzer Generals should be around skill 6-8 or higher. As a stopgap measure, I have a 3 or 6 Cavalry divisions who guard the flanks of armour. This means that the armoured formations can push farther behind enemy lines without waiting for the slow INF to catch up.
About TC: It's not really an issues unless you are going for full world conquest or you really fuck up your game somehow or you play as a minor. If I play as either USA or USSR, there will never be TC issues. If I play as Germany, I use '36 and '37 to build more IC which helps with the TC before war. During war, steady supply of GAR
P-divions in a spiderweb keeps the partisans low and their burden on TC minimal. Never keep airfields or ports in pool for long, they really place a burden on TC and you don't want to keep any units in the pool for extended periods.
Also, you can safely go somewhat over TC, it just means that your ESE drops. When you have good infrastructure under your units (like most of Europe) it's not a problem at all. It becomes an issue in Africa and parts of Asia but you can circumvent that with offensive supply for 30 days at a time if your supply pool can take the hit. It's only a problem when you go seriously over the TC, because then ESE might drop into 50% or so, which signals serious problems for your units since ESE determines how fast they regain ORG.
Gah, sorry about the wall of text. I guess I could talk about this shit forever.
I think you're losing all manpower to reinforcements or maybe you just have too many armies in the field. It's key to research those agricultural techs very early (assuming a '36 start) and they'll give you a little extra weight after 3 years.
They're both amazing games in their own ways.
