Sunkern should win. Magikarp has worse Special Defence than Sunkern, and at level 10 Sunkern gets Mega Drain, which is a super effective STAB move, which also heals it from any damage Magikarp's Tackle actually does. Magikarp's Attack is absolutely pitiful, so its Tackle shouldn't be doing much at all, even taking into consideration Sunkern's bad Defence stat. The only way Magikap might stand a chance is if it is taught Bounce (by Move Tutor) and even then, I would put my money on Sunkern to win.
I mentioned Mega Drain above, because if you caught it at level 10 in the wild, then that is the best attack it would have. If it has Energy Ball (by TM) or Giga Drain (by breeding - level up moves can be learnt through breeding) then it would probably have a much easier time against Magikarp.
The only reason Magikarp has a higher Base Stat Total than Sunkern is because of its Speed and Defence. All of its other stats are actually lower than Sunkern's are. Speed means it goes first (shouldn't really be a big deal). Defence is useless because Sunkern will probably stick to Special Attacks. So Magikarp's only semi-decent stats are actually not all that helpful in this battle.
For the above reasons I think Sunkern would win.
