Heya,
Some lights do have different output temperatures which can cause odd issues with white balance. They also have different power outputs so you have to use each one to their advantage, or at least know their limitations.
You're not necessarily making things difficult, but that depends on how you're using everything (since it's not completely clear how you've set your lights). Some example images would help here to show what you think is not good.
Have you tried each flash individually to see if there's an issue with a certain flash?
White balance can be changed in post, so no matter how cool an image appears, you can warm it up. Shoot in RAW.
Are you trying to use TTL bounce with the 270ex and then using manual on the 560II and wondering why you're getting weird results? That can definitely be an issue that you're the root cause of, if that's case. The 70D has bounce exposure TTL issues for sure (well documented underexposure when using TTL bounce specifically, it's weird). While trying to do TTL bounce and then manually add the 560II is going to give weird exposure anyways if you're not being very careful with placement and power output of your manual 560II flash. If you're doing this, I would suggest you use two ETTL flashes and use FEC to use one as key and one as fill. Or, just use both in manual mode and manually set one as key and one as fill, or both as fill.
Placement matters. The closer your light to subject, the higher it's output. This changes your power levels immediately if you move relative to the subject(s).
When bouncing, the surface will give your light a color. Bouncing two different surfaces will give you blends. Keep this in mind.
Personally I would have no problem using the two lights together you're using, but I'd use them both manual and I'd use one as key (on camera bouncing) and one as room fill at a low setting--paying careful attention to not create weird shadows with my key bounce; Example: I'd first set the 560II off camera some where in the room and point it at the ceiling and do an exposure of the room without the 270EX involved, to get a gentle fill exposure value dialed in. I would leave that one constant. Then, add the 270EX as a key (you could use ETTL on this one if you wanted to make up for your moving around and the distance from flash to bounce surface to subject angles change drastically quickly and that's where TTL really is a time saver). If not much is changing you can use it manually to get the ideal exposure values.
If I were in your shoes and were replacing both lights, I'd replace them with two off-camera ETTL/HSS capable lights, like Yongnuo 685's with a 622-TX controller on the camera.
Very best,
