iitjee 2001 question

i think it would be the first one because
1.) it has more no. of basic sites (i.e. two nitrogen with lone pairs)
2.) its conjugate acid is resonance stabilised

i think it should be second one because if we apply the same concept as in aliphatic amine vs. aromatic amine comparison of basicity , the lone pair of ntrogen in the first one is in conjugation with double bond, however it is readily available for donation in the second one, supported by +I effect

first one will be more basic ,
and the proton will be accepted by the nitrogen attached to the carbon with double bond ,
bcz, when it will accept a proton, the pi bond will shift towards nitrogen and the carbon will get a +ve charge wich will be stabilized by +M of 2 nitrogens ....
this reaction is like addition of H+ across an alkene ...

Adding to qwerty's answer, the second one also has steric hindrance in comparison to the first one. The two methyl groups(believe it or not) block out chances of the proton attacking nitrogen's lone pair.