Reaction speed of Na2CO3 with vinegar vs that produced by NaHCO3 with CH3COOH
Sodium carbonate, $\ce{Na2CO3}$, will not create gas when mixed with an equimolar  portion of acetic acid (i.e. $1\  mol\ \ce{Na2CO3}:1\ mol\ \ce{CH3COOH}$). The reaction would proceed as follows: $$\ce{Na2CO3} + \ce{CH3COOH} \ce{-&gt;} \ce{NaHCO3} + \ce{CH3COONa}.$$ Therefore, you would need another equimolar portion of acetic acid to protonate the bicarbonate ion, according to this reaction: $$ \ce{NaHCO3} + \ce{CH3COOH} \ce{-&gt;} \ce{CH3COONa} + \ce{H2O} + \ce{CO2_{(g)}}.$$ This should illustrate that using sodium carbonate simply causes you to use an extra portion of acetic acid to make the same amount of gas. 

Thus, sodium bicarbonate and acetic acid will produce gas in less overall time than sodium carbonate and acetic acid. When starting from sodium carbonate, the reaction will proceed through both reactions above. When starting with sodium bicarbonate, only the second reaction must proceed. Technically, the rate of gas evolution will be the same once gas formation begins (assuming equal starting molarities). However, the sodium carbonate reaction wouldn't produce any gas until the first reaction had completely finished, taking more time overall.