If I am playing with the Eastern Front option, I do tend to send about 1/2 of my transports a East. I send a lot of my level bomber and remaining patrol gruppes as well once I get past the Allied D-Day invasion and if those units aren't worn down by then. However, I tend to keep the tactical bombers and enough level bombers for counterattacks and to keep the Allied fighters from going all-in on ground support/interdiction/escort.
There is an AP cost to moving air units to the Eastern Front, so I only move units that are pretty much full strength and gruppe-sized. It costs the same 1 AP to move a 30-48 plane gruppe as it does to move a 3-4 plane unit or a gruppe that has been worn down to 8-10 pilots, and it makes a much bigger difference in Eastern Front strength.
Not involving aircraft, but I also usually send WBMeF Holland and Belgium east, once I have made alternate command arrangements in the West. Those help the Eastern Front too. I also move corps HQs with bad commanders east and get other corps HQs from the east in return. Generally you get acceptable to excellent corps commanders back on the corps HQs you bring west in return. That may be a bit cheesey and in need of a fix by the developers, because swapping badly-lead western corps for better-led eastern corps is much cheaper than the AP cost of just replacing the commanders of the poor western corps. You can argue that you don't get your choice of commander on the corps coming from east to west, and that is true. And you don't want to get into the AP cost cycle of sending a corps HQ east, getting a poorly-led corps from the eastern front in return, having to send that corps HQ back east, draw another corps HQ from the east and hope you get a decent commander this time, etc.
In case you haven't noticed, the game changes the commander that is assigned to an eastern front corps/army in the original scenario setup, and kind of randomly replaces it with another commander, so it doesn't do much good to look at the HQ/leader database and say "Aha!! That corps is lead by a 8-7-7-6 7 mech/7 infantry commander, so I will be sure to grab that corps for the Western Front!!" You're not going to get that leader if you select that HQ.
I tend to pull mountain divisions, infantry divisions, some corps HQs, some fighter gruppes and maybe an army HQ from the East. I stay away from moving mechanized units from the east (they have a 2X strength bonus there, vs. just normal 1X strength for non-motorized infantry and mountain units, so moving the panzers/panzergrenadiers west drains eastern front strength very badly.) I'm tempted to pull some mixed flak battalions or regiments from the east, but those cost almost as much to move west as an infantry or mountain division or corps HQ, so I stick with the larger units. Maybe I will try to grab a few flak regiments from the eastern front and attach those to some western front divisions. Overkill maybe, but I suspect that it costs as much to grab a flak regiment from the east as it does to get a mixed flak battalion.
Between the Eastern Front requiring APs to move units there and more APs to move units west, and the Eastern Front's tendency to grab what would otherwise be your accumulated replacements on the Western Front to reinforce the battered units facing the Stalinist hordes, checking the Eastern Front box is not a god-send. However, I like playing with it. Keeping the Eastern Front from completely collapsing adds to the atmosphere and challenge of the game, and you get some useful units back west in return for the reinforcements you send east.