IMHO, it really depends on your stats. If your overall GPA is a 3.7, and haven't taken any science classes, why put yourself through taking all those science prereqs beyond the basics? I would only recommend the extra degree if your GPA or science GPA is on the fence or in the crapper and taking a bunch of science classes will really boost it. This is one of the reasons that I am doing a second degree (both GPAs are in the crapper).
Also, you can use that time you'd be in those extra classes to get yourself some killer medical experience, which will make a difference, provided you have the other required stats.
Finally, adcoms don't really care whether you get the second degree or not. But I do agree with LoneCoyote - having that science degree will come in handy if you want employment experience before med school, and it does depend on your personal preference.
Good luck! 👍