Would suggest to go against the Biz since their are usually tougher than the Egyptians. Egyptians army is often huge but it is usually a rable. Likewise their generals are not as good as the Byz. The Egyptians do get at least a couple of very good ones general but the AI can be dumb enough to put them in a stack with a two stars king (same is true for the Byz but the emperor has very often at least five stars). Getting to Egyptians to go into civil war is also much easier.
If you go after the Byz, you need to make sure that you have a good chance of getting rid of their fleet (if they win the naval battel be prepared for all sorts of trouble). Once you have destroyed their fleet, take their three island (usually poorly defended). You can keep those without too much trouble if the link between them and your king is not cut by an enemy fleet. Those island usually have inns that can turn handy for hiring mounted crossbowmen. I am not a huge fan of those but they are a big bonus agaisnt the byz since it is not uncommon to see a byz province with an eight-star general as its sole garrison. IF you launch a regular attack the AI will pull out but if you only attack with one or two units of MC, the AI will accept the fight. Provided you do not make any blunder, you can easily kill the high value general with a little patience (shoot, run away, shoot, etc.). Even if you fail, you've only lost an expendable unit
Besides what Lord of the Storm already told you, keep you infantry grouped as much as possible (no point chasing routers for long with those, they will only catch a few and get exhausted in the process, only do it if the AI has no reinforcement of substance), do not let you cavalary get exhausted chasing three archers, remember that the pause button is your friend.
Hope it helps,
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