I've studied both. Both have upsides and downsides. Don't be discouraged by the amount of Chinese characters as you'll be introduced to pinyin as a romanised way to pronounce their words. You'll eventually pick up a lot of characters while learning vocabulary. Chinese is also more similar to English in grammar as they use subject-verb-object sentences. There is also a lot of use to studying Chinese characters as they are the basis of a lot of East Asian languages, including Korean.
Korean has an easy enough alphabet to learn so you can quickly learn to phonetically say written things. But their grammar and spelling is quite difficult. Plus their typing is completely original and you'd have to learn how to type again. There's also a lot of similarities to Japanese, like their use of particles and honorific conjugation.
Since both Chinese or Korean have a lot in common I think you could start with either one and it would help with the other. I'd recommend Chinese simply because you'd have more opportunities to use it abroad in your home country. Plus S. Korea's western worker market is shrinking with stagnant wages and soaring house prices. China seems to be the hot new place for westeen foreigners to emigrate.