I squish them and they never come back. :) I do this daily when the tomato plants are small, but when they are overgrowing their cages with bountiful leaves, I'm less anal about keeping a daily aphid-smooshing routine. :)

A weak solution of dish soap works but killing them by hand is what I do these days. I had a lot of aphids on my tomato when I transplanted them out so I killed as many as I could find by hand twice a week. Once the plants start to take off I no longer notice much aphids on there. I would suggest making sure your plants are as healthy and vigorous as possible because healthy tomato plants can easily outgrow limited amount of aphid damage.

I am more concerned about aphids if I see them on my rose bushes.

The excess nitrogen your tomatoes are getting is more harmful than the aphids. Fix the fertilizer problem and the aphids will go away.