I mean, you are only going to use one rarity in the end, and the higher rarity is always better. So just rank up and use the 6 star
If the champion needs to awakened, it's always better to rank-up the 5* (Omega Red, Aegon, Nick Fury,...). If the sig ability is optional, then it's always better to rank-up the 6* (Magneto, Warlock, Human Torch,...). But only rank-up the 6* if they are really really good. T5b and T2a, although more available recently, is still fairly costly. You can R5 two 5* for 1.5 R2 6*. That starts to count.
It really depends on the champs. If they need high sig the 5 star is always a better option (unless you have 100+ 6 star sig stones). Another reason you might wanna rank both is if they are a core part of your questing team, but you also want them for aq/aw. For example if you almost always bring doom on your questing team if you have a 6 star and a 5 star you can continue to quest with one while using it to attack or defend in Aw.
You have to tell us who the specific champions are and if they’re awakened or not. It’s definitely worth upgrading both the 5* and 6* version of some but not others so it completely depends on the champion.