They don't really replicate real scanlines very well. I've only personally used an SLG-3000, but there isn't anything much different the others could do that it doesn't.
If you must display 240p on a flat-panel, HLSL will give you much better results from MAME than a hardware solution. If not using MAME, hardware is sometimes the only option. A high-quality upscaler like an X-RGB mini may do a better job, not sure. Pretty pricey anyways.
1080i is not so hot either. Sounds like you're just using what's lying around. It's likely to be laggy and very poor for gaming anyhow.