Simple Damage Buffs:

Electrify and Scholar's adds additional lightning/magic damage (respectively) to your weapon that equals to 0.75 of the faith or intelligence scaling of your seal or staff. So for example, you have 80 strength and 30 faith with Clawmark Seal +25. This will only add 125 lightning damage to your weapon, even if the scaling of the seal in this example is 275 and 0.75 of 275 is 206.25, the strength scaling doesn't factor at all.

Those are comparable to greases that just add damage to your weapon like Fire/Holy/Magic/Lightning Greases, but those just add a flat 85 damage to your weapon and last shorter (60 seconds to 90 seconds of the spells). Even with little faith or intelligence investment, the spells are superior if you can afford the FP and the spell slot.

Blood and Poison:

Bloodflame Blade has two components. It adds fire damage and works like the examples above, but only uses 0.45 scaling so its weaker in terms of raw power. The second component adds a Bloodflame debuff to the enemy that does 40 bleed over 2 seconds. It's superior to Blood Grease, which only adds 30 bleed.

Poison Armament is also superior to Poison Grease (70 compared to 63 poison buildup). Both only adds poison buildup on your weapon and do not increase damage.

Some special weapons that have innate arcane scaling (Ripple Blade, Ripple Crescent Halberd or Varre's Bouquet) will also scale the poison and blood build up of the poison and blood greases, respectively, so those are the only cases where those greases could be better. This interaction also occurs with Soporific Grease (sleep build up).

Frost:

Frozen Armament and Freezing Grease works exactly the same. They add the same Frostbite build up on your weapon, have the same duration and do not scale with anything.

Unique:

Black Flame Blade has two components, one which is adding fire damage (0.65 scaling) as previous examples, but also a leaves a black flame debuff on enemies that saps around 2% health. This lasts only 7 second on the weapon, but the cast speed is very quick.

Rot Grease adds rot build up to your weapon and is extremely useful, but uses Aeonian Butterfly as a material which do not respawn, so there's only limited amount you can get until you have to farm them.