There has been surprisingly little research on the topic, and as might be expected given the lack if new data, recent studies have not supported a general libido lowering effect of vasectomy. A study in Brazil from 2005 looked at 64 patients undergoing vasectomy and found a small but statistically significant (at p < 0.001) improvement in international index of erectile function scores driven by increases in desire and sexual satisfaction. However, it should be noted that while 67% had improved scores, 17% had worse scores, 16% reported no change (Botero et al, Braz J Urol. Sep-Oct 2005;31(5):452-8)
Orr and Moore found from a group of 1000 consecutive vasectomies that only 1% reported "psycho-sexual problems such as decreased libido, ejaculatory problems, depression" (r Med J. 1989 Feb;82(1):19-20.) However this analysis appeared to be more focused on detecting surgical complications.
Islam et al. (Bangladesh Med Res Counc Bull. 1991 Jun;17(1):17-22.) did a follow-up study of 300 tubectomy and 300 vasectomy cases from urban and rural parts of the Mymensingh district in Bangladesh. They found no significant effect on libido in either group, though I was not able to examine the instrument used to survey patients.
It should be noted the same critique may be made of the Dias article referenced by wikipedia (Acta Psychiatr Scand. 1983 May;67(5):333-8). However like the Islam et al. article, I was able to find the abstract online. The Nielsen and Genster article cited in wikipedia is in Danish, and furthermore no abstract is available online in any language. Thus it requires access to a paper copy to know what it reports, let alone its methods. It does not appear to be available in the holdings at the the University of Washington Health Sciences library, the most comprehensive journal source available to me. Thus I cannot assess it.
It should also be noted that there are other reports of similar age as the two referenced in wikipedia that address libido and vasectomy. For example, Jackson and Avant (J R Coll Gen Pract. 1982 Mar; 32(236): 172–173) looked at 2000 men on follow-up fron vasectomy with a very brief 3 question questionnaire that asked one question (with follow up to explain positive or negative answers) about the effects in their mental health. Twelve men reported decreased sexual drive but did not regret the procedure. Katila and Rimón (oz Praventivmed. 1979 Oct;24(5):346-8) found on follow-up of 107 men average 4.7 yrs after vasectomy that only 2% were dissatisfied with results. 32% reported improved 'sexual potency' while 3% reported impairment of sexual function. Thus the articles cited in wikipedia are by no means the only data available. Nor are they completely typical of the data at the time of publication except in that some papers reported a tendency towards worse function and others improved.
Finally, in regards to who might more likely to report worse libido after vasectomy, Buchholz et al. (J Psychosom Res. 1994 Oct;38(7):759-62) looked at 45 men chosen at random from a vasectomized group of 254 men, as well as 18 men from a group of 180 men with erectile dysfunction who attributed their dysfunction to a vasectomy. They "analysed the social background, motivation for vasectomy and postoperative changes of sexual life or behaviour of the partners. The partnership constellation, particularly the role of a predominant female partner seems to be an important feature for vasectomy acceptance. Low acceptance might cause erectile dysfunction." Essentially, they found that when men were getting a vasectomy felt it was being imposed on them by their partner, they were more likely to report dysfunction. When the men reported they wanted the vasectomy, they were more likely to report improved sexual function.
In general the recommendation for pre-vasectomy education is to note that evidence does not support the idea that vasectomy changes sexual function See example by J Murtagh (Aust Fam Physician. 1993 May;22(5):806) or Mayo clinic patient education (see https://www.mayoclinic.org/tests-procedures/vasectomy/about/pac-20384580).
Most recent research on libido and male contraception has focused on the effects of proposed chemical contraception in males, such as with low dose testosterone.
My own reading of the literature suggests that older articles tend to report more negative effects on libido compared to more recent ones though the amount of data is unimpressive. If this qualitative trend really is present (and this assessment is extremely subjective not at all a quantitative assessment such as with a meta analysis), it could just as easily represent changes in attitudes and expectations about vasectomy as direct physiologic effects of the procedure. Indeed this would be my working hypothesis, though it should be noted I an a psychiatrist and neuroscientist and as such am likely biased towards this hypothesis.