For what it's worth, Fat-beams seem to have even less tension than Sunbeams, are rougher in texture (stainless vs nickel), and sound a bit more scooped (more lows and highs). These properties make them fun to slap, but are also very expressive fingerstyle. Marcus Miller obviously demos what they can do in competent hands with the right preamp and EQ.
Being nickel, Sunbeams are arguably easier to play and a bit less aggressive, especially the top end. I like both depending on the situation.
Both will have less tension than the EB Slinkys you were using. But I think the EBs would qualify as "punchier" strings overall.
Strings are a very personal choice.