Based on the community feedback here, the DA 18-135mm is generally a solid, practical lens, but it does get softer in the corners at the long end. The specific comparison given was that its telephoto-end corner sharpness is weaker than a higher-end DA* 50-135mm, which suggests you should not expect top-tier edge performance at 135mm.

For your question versus the 18-55mm: the provided answers do not establish a clear, measurable resolution win for the 18-135mm over the kit lens. The main takeaway is that the 18-135mm is considered “good enough” optically while offering a much more useful zoom range, which is why it often gets used more in practice.

So if your priority is convenience and range, the 18-135mm is a worthwhile walkaround option. If your priority is absolute corner sharpness—especially wide open at the telephoto end—you should expect some softness and not assume it will clearly outperform the 18-55mm in every part of the frame.