The solid rod will be stronger than the tube-comparing diameter to diameter. However, the added weight of the solid rod is proably not worth the added strength. The strength comes from a combination of wall thickness and diameter. If you are concerned about the bending, just keep the same wall thickness and go to a larger diameter.

I don't see why it would need to be seamless. The weld should be as strong as the adjoining material. These are full penetration welds. The only issue may come in when the bar is polished-you could see a slight line.