I thought I'd make a short post on this topic as I've had a number of PMs and e-mails of late for advice on rods (around PE10) that are good for both big chuggers and stickbaits. The unfortunate reality is that if you're referring to surface stickbaits, this rod does not exist.
Very few manufacturers produce specialist stickbait rods. In fact, I can only think of Carpenter and Ripple Fisher. Specialist stickbait rods do not go beyond PE8 at this point as the need for a flexible tip to impart the necessary action has yet to see either manufacturer get to a PE10 rod that is suitable.
If you're looking at sinking stickbaits like an Orion Bigfoot, you can get away with a rod designed primarily for chuggers. If you want to use surface stickbaits, however, ideally, you need a stickbait rod - and these do not currently come heavier than PE8.
Surface stickbaits are a real specialised type of lure and are really only suitable for calm conditions. That is not to say you can't cast out a Carpenter Gamma on a stiff-tipped popping rod like a SP78EXH. It is that you will have trouble trying to impart that darting action on the surface which the lure is designed for.
