All three have its pro and contra, but as they are mostly Soldiers with another mastery, they are also to a certain degree similar. However, each mastery combination has its own resulting synergie and the three budget builds also have a slightly different focus, my Witchblade and Battlemage are more defensive orientated, while Warlord has a more offensive setup. Warlord and Witchblade are likely also a bit easier to play as the battlemage uses as gimmick more offensive skills. Both are likely also a bit stronger. The Witchblade and its stronger defense focus might be a bit more forgiving (and therefore beginner friendly) - the Warlord should have the even easier gameplay. However, the likely currently (1.1.9.3) strongest S&B budget build should be a Blade Arc Warlord.
Another factor you should consider is however also the intented target build, and in this regard Battlemage is often considered as weaker class (single resist reduction (RR) - but there is a specific legendary set supporting physical overguard S&B gameplay allowing not so bad results (Spellscourge)). Witchblade can us RR from both masteries (not used for the budget build) and Warlord (also RR in both masteries) is certainly the most flexible and natural class for S&B gameplay.