"Tubes are generally better at voltage drive while SS is better at current" and to finish this statement,voltage driven produces even harmonics as opposed to SS which produces uneven harmonics.
Depending on who you talk to, this statement is likely to be considered a half truth. Part of why has to do with terminology.
The first part is where there is confusing use of terms. 'Voltage Drive', if we are using the Voltage Paradigm (see http://www.atma-sphere.com/Resources/Paradigms_in_Amplifier_Design.php) often means that the amp is capable of constant voltage regardless of load. If you do the math, this means it has a lot of current. OTOH, 'better at current' sort of means the same thing. So one must be careful to winnow out the exact meaning from the first part of the statement.
The latter half is 1/2 correct. Even-ordered harmonics will be present if there is also single-ended circuitry and has nothing to do with being 'voltage driven'. This may or may not be the case with tubes; our amps for example are fully differential and so do not produce even-ordered harmonics (a fully differential amp will produce mostly the 3rd harmonic).
It is true though that regardless of the topology, transistor circuits will produce odd-ordered harmonics and at any power level. This is due to non-linear capacitive elements inherent in the junctions of the semiconductors and also due to inherent nonlinearities in the devices themselves (certain FETs being less prone to the latter problem). Loop feedback is often used to control the latter phenomena, but said use will also guarantee odd-ordered harmonic distortion as it is a product of the use of loop negative feedback in an amplifier design.