It largely depends on the organization in which you wrestle for, but i will answer this question in general.
Cutting a promo will get you farther in your career, as wrestling is an individual sport for the most part, meaning that you must sell yourself in order to get yourself over, which is accomplished through cutting promos in wrestling. The majority of the wrestling fans in the united states I would argue are not as intamate with the facets of what makes a good wrestling match as some of us more informed "wrestling fans" who can voice our opinion on the internet. What I am saying is that Anyone can realize the greatness of mike skill. It is very easy to recognize when an wrestler has the crowd in the palm of their hand by boo or cheer, and those good on the mike can play to emotions to make a crowd ignite. Anyone can take offense to a heel comment or laugh at a witty putdown or get riled up by charisma without thinking. Since it takes no knowledge of wrestling to judge mike skill, this is oftentimes what decides if an wrestler is "over" or not, as the majority listen to a wrestler, and his words are what buys the t shirts and sells the tickets. Either fans will come in support of the wrestler or see if the cocky heel gets his *** kicked or can back himself up. The audience dictates the show and hence will be pushed accordingly, as like any business the WWE will push on performance level.
Now for a wrestler's legacy, I will argue wrestling skill is more important. For instance, Shawn Michaels is great at generating heat with his pre christ dislikable attitude and ability to get under people's skin, and the edginess helped carve the attitude era with DX, yet it is Shawn's ability to put on a clinic of a wrestling match with charisma and storytelling that puts him in a truely special place among the greats in recent wrestling history. The undertaker is pretty good on the mike, but Taker's ability to adapt his character to avoid it getting stale has been achieved through storyline but in ring moveset and mannerism changes, and one of the largest reasons Taker is considered the potential GOAT is the amazing matches involving the likes of Shawn Michaels, HHH, Kurt Angle, Bret Hart, Mankind and so on. Taker is not remembered as much for say the promos he cuts before casket matches, but more for moments like throwing Mick Foley off a cell. No one cares about Taker's character promos to intimidate his wrestlemania foes, they anticipate the annual great match of the year canidate he puts on at mania, achieved through his IN RING sense of timing, storytelling and special moveset he mixes with his character. Chris Benoit is beaten by Santino Morrella in the mike department, but because Chris is such an fantastic wrestler, he has his place among the great storytelling and technical legends, as do people like Bret Hart and Dynamite Kid who all aren't great on the mike, but are fantastic in the ring and are legends accordingly. Wrestling is the name of the entertainment, and while it is easy to weed out those who can just talk and stick them in a midcard role, it is much harder to hold down those who can wrestle. My final point on this is that if you look at wrestling totality, many puroresu legends are seen as perhaps the greatest ever, not because of promo and segments, but because of their ability to wrestle.
In closing: For career success, it is more important to cut a promo, but for legacy sake, it is more important to wrestle.
