Ive only played WiF. I played TR for a few minutes but didnt like the clutter appearence.
Lessons i learnt.
Be prepared to find long losing battles on one siode of front so can win on other.
Dont overstack your advancing columns cause the computer will strategically counterattack. Need to atleast make a fight of it.
Altho you can get bogged down in a fight for a month you can also blitzkrieg so sometimes its worth going if your a bit unprepared aslong as enemy is also. (enemy retereated after losing a battle and has vbeen harassed by aircraft).
WiF gives the computer time to manuvuer in defense but even on very hard it still gives you time. Dont panic with bad looking bars like 80-90% vs you, Still have time for manuvuers.
Amphius assaults are very useful. They have brought me quickest strategical victorys. (Landing in athens and crete - Landing in suez on septemper the 2nd

) Dont actually assault tho unless have marines

.
Improve infrastructure in places that prolonged battles will occur. Or the staging points for major offenses. Had armoured fist in oppeln for attack on poland with improved infrastructure. Stuttgart to manuvuer left and right. Infrastrucure is pretty fairly priced in my opinion.
Airbases are probably good to build after get all technologys. But they are a little to expensive for my liking. But if intend a major long term offensive in area with few airfields then .......
Wif has mass air formation effectively in sky of 8 with a airmarshall. Make sure to use this effectively and dont suffer overstacking its very annoying. I find spreading 8 formations to seperate battle areas with a airmarshall in the mix is a decent way. Can if bothered stagger arrival of planes throughout day. But im usually not that bothered. Spreading them out and possibly bombing through night keeps rid of that naughty overstacking.
Dont let the computer retreat to citys! If avoidable cut off retreat to citys. I once let 38 infantry divisions retreat to warsaw. Even surronded with 50 quality divisions on it. i felt like crying

. When attacking just dont let them congregate like this. Breaks heart to try and win these battles.
WiF can seem like slow battles. But the speed of the units is quite fast. So if you get a flanking force like a ball on chain and really go for it can achieve amazing things still, Thats what i love. It still heavily rewards the well planned offensive
On very hard WiF eats your manpower so much

You get less to start with and units cost more

So get the argrichemistry stuff check each year for manpower ministers. GET ALL THE MANPOWER CAN! In the very end manpower is real constraint on army power. If dont have alot of manpower replace these men with technology. Offcoures with the TC load this can only go so far.
As for engineer brigades they are still lovely but they do eat manpower. 2.5 manpower a brigade. I love them especially the +4 speed increase is massive but give them only to a specialised army for river crossing or your armoured spearhead. But not to many cause of eternal manpower problems
In summary fight hard and use force multipliers like aircraft, manuveurablity, concentrated force amphious assaults and always the unexpected
many regards pollock