Assuming you have the budget for the 15-85mm (almost twice the price of the 18-135mm) I'd recommend the 15-85mm lens over the 18-135mm. Why?

• It has better reach on the wide angle which you wouldn't be able to cover with your 18-135mm + 55-250mm combo. A lot of lenses cover up-to 85mm but none of them goes down to 15mm.
• It has better image quality and able to render very good colors.
• It's sharpness is comparable to any L grade lens, on the other hand, the 18-135mm is much softer.
• It has Canons top of the line USM focus motor, which is faster and quieter. The 18-135mm doesn't have USM and makes sound while focusing.
• It has non rotating front element and also the focus ring doesn't rotate while focusing, a automatic choice for filter users. The 18-135mm also has a non-rotating front but the focus ring moves during AF.
• It provides FTM (full time manual focus), handy feature for fine-tuning or doing focus adjustments quickly.
• It's build quality is better and also has focus distance meter.

ISO 12233 Chart 100% crop comparison between the 15-85mm and the 18-135mm, please refer to this link. Compare at different focal lengths and see the difference for yourself.

Overall, the 15-85mm is a better built, better performing and better featured lens comparing to the 18-135mm in almost every aspect. It also weighs more, costs more and having a larger filter thread (72mm over 67mm) makes the filters expensive. Once you get used to the quality this lens provide, you might even consider replacing your 55-250mm lens with may be a 70-200mm f/4 (mayybe) ;)