Why does the client have ae2 but the server doesn't?
The error message you show in that screenshot means one of your mods has broken networking.
It does not say which mod.
Usually, the only way you find the problem mod is to experiment with removing mods until the problem goes away.
Backup your world or experiment with a new world/save when doing this.
I do see a tonne of errors where it looks like it is having problems processing recipes and loot tables sent by the server?
The most notable problems (the ones towards the end) would be:
Some incompatiblity between JEI and extreme reactors.
tinkers construct recipe error:
and what looks like the twighlight forest patchouli book:
I can't though say any of these are the definitive cause of the problem. Since none of these are directly related with or going to the nether.