They're not the same. They have the same grammar, but a lot of different words. The pronunciation is very different, although if you can speak the Spanish of Spain, you can perfectly understand the Latin Spanish. I recommend you to learn the Spanish Spain, because the pronunciation is easier (in my opinion), and it's very useful: the Spanish is the second most spoken language, below Chinese and above English. I hope this could help you!

Grammar is the same but some words are differents, there are words that doesn't exist here in Spain but are typical in Latin America. The accent is different too, but in spanish there are so many accents. Both spanish could help you to understand spanish, the big different would be the accent I think.

I think its like American English vs Britan English... they undestand each other but some words are different or they have different meaning in America or GB. Depends where are you from, if you are closer with Latin people than maybe it's better that you learn Latin Spanish but if you are closer to Europe and Spain, than it's better your choice is Spanish from Spain. Whatever you choose, you gonna be understood and I'm sure you wont have big problems.

grammatically are the same but we have different cultures, therefore you will find different idioms and accents. You can choose any, I'm sure that you don't have problems and you will be able to learn new vocabulary in every place that you visit.

I would agree with Andrea. I have communicated with a few people from Spain and some from Mexico or latin America. There are word differences as well as accents. Example: In Spain- please correct me if I am incorrect native Spanish speakers-for instance Frozen is Congelada for Spain area but Latin America/Mexico say helado. I watch a lot of Frozen and have started listening to it in Spanish for some variation as it gets old to watch almost 24 hours a day that we were watching it.