Medical care is of a generally excellent standard in Thailand. I can’t speak for Bali, but this won’t be a problem in Thailand. However, consider a larger city rather than living on an island. Koh Samui has well stocked 24 hour pharmacies, often staffed by a nurse, but it’s a long way (a boat ride plus a long bus ride) to the nearest major hospital in Surat Thani. The other option is to fly to Bangkok. An island is just not a great place to be if you have a serious, life-threatening emergency. Living on an island also drives up the price of everything, because it has to come by plane or boat. Sure, the island lifestyle is idyllic, but it will cost you.
On the mainland, when you say “southern Thailand,” it really depends where you mean specifically. On the mainland, the closer south from Phuket you get to the Malaysian border, the more dangerous it becomes (Phuket is safe and affordable). Kidnappings and bombings carried out by Muslim separatist groups are not uncommon. You don’t hear about this much in the Western media, but it’s well known locally. It’s also less expensive in these parts of Thailand, and the pace of life is slower and quieter. Because of the security threat, there are a lot of relatively unspoiled and beautiful beaches. It is best to dress modestly in accordance with local religious customs, though.