Apparently there are two conventions for the (1,3) tensor called the Riemann curvature and they give opposite functions $$T_p M \times T_p M \times T_p M \to T_p M :$$ $$ (x,y,z)\mapsto R(x,y)z.$$
Below I will use the definition via vector fields (capital letter $X$ versus vector written in lowercase $x$) because it is widespread, though I much prefer the interpretation via first-order infinitesimal holonomy $M(x,y)$.*
In Kobayashi-Nomizu [Foundations of Differential Geometry], Schouten [Ricci calculus], an article of Nurowski in Journal of Geometrical analysis, Loring W. Tu [Differential Geometry], Michor [Topics in Differential Geometry], Szekeres [A course in Modern Mathematical Physics], Chern Chen Lam [Lectures on Differential Geometry], Sternberg [Lectures on Differential Geometry], Weyl [Space-Time-Matter], Spivak [A Comprehensive Introduction to Differential Geometry], John M. Lee [Introduction to Riemannian Manifolds], in several articles in Wikipedia, they use conventions so that $$R(X,Y) = [\nabla_X,\nabla_Y] - \nabla_{[X,Y]}.$$ Then $M(x,y) = -R(x,y)$.
In Arthur L. Besse [Einstein Manifolds], Berger Gauduchon Mazet [Le spectre d'une variété Riemannienne], Bishop Goldberg [Tensor analysis on Manifolds], Lovelock and Rund [Tensors, Differential Forms and Variational Principles], Gallot Hulin Lafontaine** [Riemannian Geometry] they use the other convention $$R(X,Y) = \nabla_{[X,Y]} - [\nabla_X,\nabla_Y].$$ Then $M(x,y) = R(x,y)$.
From my own sample above, I have the impression that the first one is way more frequent that the second one.
Q1. Can we say that there is an agreement today, in the mathematical community at least, on which one to prefer?
Q2. Why do most people prefer the one that gives the opposite of M(x,y)?
*: The first-order infinitesimal holonomy $M(x,y)$ is the limit endomorphism of $T_p M$ obtained by taking a small injective loop in a 2D sub-manifold directed by $x$ and $y$, following the parallel transport, subtracting identity and dividing by the signed area of the loop normalized by giving area one to the basis $(x,y)$, and the sign is w.r.t. the orientation of the basis $(x,y)$.
** their formula for $R^i_{jkl}$ seems wrong
Note: a.f.a.i.k. all references I mentioned seem to agree on the meaning of $[A,B]$ for operators (and vector fields).
Note: no, I have not read those books, just gone directly to the definitions.
In general, use the one so that your targeted audience are most familiar with.
For example, if you are a student in a Riemannian geometry course and is writing up an assignment, use the one suggested in the lecture or the textbook. If you are writing up a research paper, use the notations that other researchers in your field use. Or, if your work relies heavily on paper A, use the same convention as paper A.
For this specific problem about Curvature tensor: I have used both (not in the same paper, of course) and it does not seem to cause confusions: everyone is aware of the issue, and they all agree that at the end of the day, the sphere has positive sectional curvature.