I may be incorrect on trade name, the Mesa tube may be Sovtek versions. Made by same company as EH but the internals may be slightly different but not by much.
Depending on the amp you intend to use the EL34 in, some of the simul-class amps in 10W mode are not compatible with EL34B (based on the JJ website which may be due to different impedance of the tube, if this is true, that may also rule out use of Tung Sol EL34B). Nothing wrong with the Mesa branded EL34's. In general, I have found that the small bottle EL34 are mechanically noisy. Some of the medium sized bottle EL34 types (GL KT77, Mullard EL34, and SED EL34) do not rattle as much (the gold lion and mullards are almost noise free, the Tung Sol EL34B no rattle either). It may be hit or miss on the mechanical noise issue, that of which I have found with 6L6 tubes too, brand name is irrelevant as I have had noisy tubes with different brand names including Mesa.