Should I learn Indonesian or Malay?

They are same thing. Indonesian  (Bahasa Indonesia) is in a standardized register of the Malay language. If we take the second portion of your question (Should you learn it?) an answer might be: Maybe. There are several things to consider: Are you fluent in English? - Your asking a question on Quora indicates that the answer is probably yes. Since you are, it may not behoove you to do so, as most major companies are going to conduct  business in English, in a European language (In Indonesia, probably Dutch), in Chinese, or in Japanese. Learning one or more of those languages might be a more worthwhile option. Are you going to live or work extensively in either Indonesia or Malaysia? -  If so, then learning the language may be of benefit. If not, it may prove to be difficult to both learn the language and become fluent without daily exposure. Can you currently speak another language fluently? - If this not the case, then you may wish to carefully consider attempting to learn another. Unless you can retain the rigor which you applied to learning another language in the past in this situation, learning a difficult language may not be possible in a reasonable amount of time. Do you have the time to learn the language? - It's likely that any attempt to learn Indonesian will require a minimum 1-3 hours a DAY for several years simply to become more than conversational in it. It may take a lifetime to become as fluent as a native speaker (if you ever can) Why are you wanting to learn it? - The Malay diaspora isn't particularly large and outside of Southeast Asia you may find few , if any, opportunities to make use of your skills See also reason #1 as to why you should carefully consider why you are going to do it. If this is for personal reasons, it may prove to be beneficial; but again,it will be difficult Frankly, in my assessment (and this only that, an assessment) unless you have strong personal or business ties inside either Indonesia or Malaysia or you are going travel there extensively, it may not benefit you to learn this language. It is a difficult language to learn and it may provide you with little in the way of practicality to expend so much time and effort for something that may not gain you that much.

As a Malaysian myself, for me just pick one from 2, both is the same.But if you come to our country, even you speak in english, we still can understand. No worries.\U0001f604

Learn Indonesian because there are 250m of them as opposed to 30m Malaysians. The languages are also so similar that when you have learnt one you would have picked up the other. 

If you are fluent of english then is better to learn Indonesia language. Because Indonesian language is basically malay without to much english language influence. Some words have a different meaning but generally you could grasp the meaning it come to conversation.

Personally as a speak of bahasa malaysia or melayu. I do find that bahasa indonesia opens doors to a wider cultural experience. Speaking wise i would say bm is easier as they speak slower and more relaxed kind of feels like you're drifting on a canoe in venice. BI on the other hand is like a gattling gun they speak really fast but the good thing they are pronounced as spelt. Since more indonesian dramas get aired in malaysia and singapore as compared to vice versa. You'll find more people understanding indonesian than Malay. I guess that's all i have to say although this thread must be really old

Jan Mixon has it covered but let me add this. Given your circumstance, I would suggest not self learning but to seek out a community or an individual to not only help teach you the language but to enthrall and to inspire you with the amazing Indonesian culture. I suggest Indonesian only because i'm more familiar with it.

Bahasa Indonesia is spoken widely by around 140 million people and people who are fluent in Bahasa Indonesia will know and understand Malay but not the other way round. Bahasa Indonesia has way more vocabulary. If you need help feel free to approach us to learn. http://www.indoslang.com.sg

I live in indonesia and i lived and travel to Malaysia quite ofter for bussiness,  I speak Bahasa Indonesia, Bahasa Malaysia, Javanese, Mandarin and English.   Bahasa  Indonesia and malaysia come from the same root which is bahasa Melayu.   the biggest difference is the both language absorb other language,  bahasa indonesia is mixed of Malay 93 percent + Arabian + Dutch +  portuguese + English + Javanese + Hokkian + other local language like  sundanese while bahasa Malaysia is mixed of Malay 97 percent + English + Arabian + local malay slang if  you can speak bahasa Indonesia baku you will be able to understand  bahasa malaysia baku (standarized language) but you must learn some word  that in bahasa Indonesia is not used for example office in bahasa Malaysia is Pejabat, in bahasa Indonesia is Kantor (Dutch Origin) I  suggest you learn Bahasa Indonesia as most Indonesian can not speak  english but mostly they speak bahasa Indonesia, Indonesia has 250 million population and 17 thousand island,  the economic is growing and Government of Indonesia will ensure Bahasa  Indonesia is the only official language Malaysia has around 30  million population 60 percent malay, 30 percent chinese, 5 percent  indian.  only Malay speaks Bahasa Melayu but most malay can speak  english really well and malay people proud to speak english then malay,  even when i stayed in malaysia i speak english all the time, while  malaysian chinese / indian will more likely to speak mandarin cantonese  for chinese or tamil for indian, everytime chinese people meet foreigner  the will more likely to speak english as their malay skill is so low  even some chinese malaysian can not speak malay at all.  Malaysian  government ensure English and bahasa malaysia as their official language  but most people love to speak english then malay so just learn Bahasa Indonesia and you will be able to see new world

Interesting discussion. I don't understand either Malay or Indonesian though I am interested in Indonesian. I speak Mandarin, Cantonese, Hokkien-Taiwanese and some Teochew as well as Thai. What I can add is that the "how similar is X to Y" is somewhat subjective and depends on experience. My Teochew speaking friend tells me that he could understand Hokkien fairly well the first time he went to Taiwan. I can say about anything to him in Hokkien and he understands. He tells me his Mom is quite the opposite, she can't even understand the varieties of Chaozhou. My own Mom was like this too. She had a very hard time understanding non-native English speaker whereas I had very little difficulty. There are two factors: experience and talent. Some people are more linguistically rigid and they are going to have difficulty adapting. This tends to get worse the older you get. The same thing applies between Thai and Lao. Thai is the big language and they tend to have more trouble understanding Lao than vice versa. Here the reasons are Thai is the big language from the rich country, they don't have to try so hard to learn Lao, whereas for Lao's it's more important that they can understand Thai. Last thing to add is Mandarin to Cantonese to Hokkien. All 3 are so different that if you know 1 and want to know one of the others you won't find your study time cut all that much. Maybe 20% or 30% of your time investment at most. Between Hokkien and Teochew there is substantial commonality (both are Minnan languages) so the situation is similar to Portuguese and Spanish, or Indonesia and Malay or Lao and Thai. So to get back to Indonesian and Malay, how hard one is to know if you know the other depends on what your talents are, how old you start and how hard you try.