The Tiger and Flak 88 use the 8,8 cm L/56, while the Elefant, Pak 43 (and Tiger II) use the 8,8 cm L/71, which means longer barrel with a considerably taller and wider cartridge and therefore more penetration power.
As how the Flak 88 would behave ingame: There's a good chance we see it in the next expansion, The Western Front Armies, again. CoH isn't known to be very realistic, so there's not really a point to guess how it would behave ingame.
Thank you!
We will see, I am very excited about Western Armies! So I am patient right now!