There's a lot of marketing chatter on this topic but there is one main thing to consider; which sounds like the more attractive deal in your * specific case*?
There's an interesting Donut Hole graph from Dealicacy Showing how both can offer better value to the consumer:
The relative (%) benefit remains constant, while the absolute benefit ($ off) has a complex curve. Logically with the relative benefit it's easy to tell how much of a benefit you're getting; it's always the same, it just scales to what you buy. But with the absolute benefit you always know what you're getting. Never underestimate the power of less thinking.
A marketing study conducted by Evo A/B tested relative vs absolute benefits and found the following results:
- $50-Off Coupon generated 170% more revenue than the 15%-Off Coupon.
- $50-Off Coupon had 72% higher conversion rate.
I think the issue here is twofold; as mentioned, it's easy to understand how much I'm saving if you say I save $50: I save $50. Additionally, 15% really doesn't sound like much.
Consider the following bargains, both yielding equal savings on a certain product: 75% off or $5 off. Clearly the value of the relative benefit seems higher. Roughly speaking, a benefit of 40% or more starts to sound pretty significant. A dollar amount of $50 or more sounds significant.
If one value clearly appears to be a better value, it's probably best to offer that option as long as it's not misleading (like the terrible, lying asterisk in your question). Otherwise it would probably be best to A/B test your specific case if there's no clear winner.