I switch tire and wheel sizes quite a bit on my mixed condition bike. I have a custom bike and it was built around performing best (handling wise and rough road wise) with 700x38 and 650x42 setups. In 650x42 mode, the wheel diameter is closer to the equivalent to a 700x25mm setup, so the trail is lower and consequently handles a little quicker and snappier. One thing I have found using the smaller wheel size with wider tires (42mm) is that: even though the trail is reduced and the steering is quicker, this effect is somewhat offset with the extra rubber on the ground - so the quicker steering settles down with the more "grabby" rubber on the ground and you get the benefits of more natural turning and retaining the snappy bike feel - plus the volume for rough surfaces.

I'm not sure what a smaller 650 setup would feel like, but I suspect the handling would be worse and maybe a little too twitchy. On the other extreme, I frequently used 650x48mm and they definitely make the bike handle different on the road. Cornering isn't as precise and the amount of rubber on the road is noticeable in terms of self-steer (depending on pressure). They perform very well in rough conditions though where volume is your friend.

Edit: keep in mind, the BB height will be a lot lower going from 700x38 to 650x38 - could be a serious pedal strike issue.

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