Riker is shown to both sleep with more women, sleep with more women as a result of the amount of time covered in the respective TOS and TNG eras, but less per episode of the series. Riker also treats his sexual partners more like objects, as seen in his treatment of Ro Laren and Deanna Troi in Conundrum, as opposed to Kirk's nasty habit of falling in love with and/ or knocking them up. So it somewhat depends on what you consider a "pick-up artist" to be; sheer numbers, numbers over a certain time-span, or the treatment of women you sleep with.
If you scroll down to the "Romance" section of Riker's Memory Alpha page, you can see that Riker slept with a maximum of 14 'women' that we know of - obviously he and Kirk could have been hosting orgies off-screen in-between episodes for all we know - during the course of TNG and the films. If we accept Riker's highest number of 14 and Kirk's highest possible number of 11, we are left with Riker sleeping with 14 people between 2364 and 2379, just shy of 1 woman a year, whereas Kirk slept with 11 women in the period pre-2265, when TOS began, 2293, when The Undiscovered Country occurred. That's 11:35 as compared to Riker's 14:15. On the other hand, if we assume for the purposes of this question that Riker and Kirk only slept with women during their respective television series - which is obviously false, but bear with me - then Kirk has 11:79 as compared to Riker's 14:178, or 7:89. So Kirk wins that battle.
All of this isn't counting books, where who knows how many women, men, transgendered species, farm animals and household objects these two - especially Riker, whose standards are never shown to be all that high - have slept with in them.