It's definitely a matter of opinion, but based on many people's experiences, as well as common sense, it's easy to say that attacking stats make a much larger difference in standard sweeping. Without Attack, you have no damage to deal, after all!
Speed only influences who gets to hit first, whereas Attack / Special Attack are your main tools for the trade. A Pokemon that's fast, but weak in attacking, is not going to sweep.
Take Serperior, for example. Yeah, with Contrary and Leaf Storm, it can sweep, but without that ability, Serperior is not going to sweep, even with that high speed stat. Instead, standard Serperior will be setting up screens or SubSeeding.
With Speed, it's ideal to create a role that revolves around and complements your other stats. Seeing as good Defenses are ideal for setup strategies, that's how regular Serperior will use their speed.
However, it's harder to define a fighter with high attack, but lower speed. It's a similar concept to Speed, where you have to develop a role to suit your other stats, but seeing as dealing damage is the only way to win with Pokemon like this, it's more of a one-way road.
One way is to Tank, which is when you take advantage of good HP and Defense to become inclined in a spectrum (Physical or Special). These Pokemon, such as Rhyperior, Gardevoir and Blissey (Sorta) are Pokemon that can survive and hit back hard, albeit going last most of the time.
Trick Room can also prove to help out Pokemon like this, but then again, that takes out the Speed issue altogether, so I won't go into detail.
If the Pokemon is slow, but has high attack, and isn't bulky enough to tank or isn't in Trick Room, the final solution is to abuse Priority attacks. Pokemon like Mamoswine have a lot of weaknesses, making them frail. Stack that with high Attack and low speed and you have a doomed sweeper. However, Mamoswine holds its own ground with Ice Shard which will always strike first, ignoring priority. This tactic weakens the foe enough to to let Mamoswine take a hit, and then hit them with a full-on attack next turn, KO'ing them.
Most slow sweepers use this tactic, or purely use Priority to pick off weakened foes. This is "Revenge-Killing". It's basically a "bottom of the barrel" resort for when the sweeper is too slow (Mamoswine, Dragonite, Kecleon) or deathly frail (Sharpedo, Weavile).
Finally if your slow sweeper cannot achieve any of this, then...Well, it can't perform on its own, and is likely a very low-grade Pokemon. Pokemon like Rampardos have incredibly high Attack. However, Rampardos also has little bulk, fairly low speed, and no Priority. This is why Rampardos is "inferior", despite 160 Base Attack.
It has been a REALLY long time since I wrote an answer this long. Sorry...xD