I have always liked how spline joints look, but I was unsure whether it would help or hurt the joint strength. Are splined miter joints stronger than other types of mitered joinery?
Yes, they are stronger Splines increase the surface area being glued,; and thus the strength of the joint. And since miter is close to being end-grain to end-grain, it can definitely benefit from reinforcement.
Not necessary in things which aren't under much stress, like small boxes and picture frames, but as you say splines can also be a decorative element.
(For large picture frames, there's a cute variant of a lap joint which looks like a miter from the front and provides lots of long-grain contact. Not that I've tried it yet.)
Not certain which joint you're referring to:
But regardless of whether you mean a true splined mitre or a keyed mitre the reinforcement does add to the joint strength.
Both increase joint strength due to three factors: structural advantage, the thickness of the wood slivers used and the glue surface area. When considering splines or keys of conventional size — roughly as in the illustration above — the splined joint is superior in all regards (being both physically stronger and providing greater surface area).
It should be mentioned, there are numerous other ways to reinforce a mitre joint, from nails driven across the joint at the most basic, through to dowelling (both hidden and shown) all the way to a few variations of blind dovetails.