I have connected in both airports and can add a few details, but like the poster above I cannot remember a couple key details.

• A problem when flying from the US is I leave my house long before the check-in window for the connecting flight so I cannot print my boarding pass at home so I always have to get the connection boarding pass after the first ticketed flights.
• My phone boarding pass was once not accepted at BKK and the connecting airline, which may have actually been Vietnam going to HAN, did not have an agent at the connections area. Since then I have printed the pass when connecting through ICN or NRT or PVG.
• IIRC many airlines, especially those with few flights out of BKK, do not have a presence at the transit area. Hopefully someone else can tell you if Vietnam has agents at the transit desks.
• IME unless your checked bag is ticketed through to the next flight you will have to leave the secure area at BKK, collect it at baggage claim and recheck it for the next flight. In SIN you can take care of that without leaving the secure area but not at BKK.
• Once I was able to get to get the boarding pass printed by a different airline in the same alliance, but once I had to exit the secure area and had to sit for hours until the KE desk opened.
• In SIN I once had an issue with an AirAsia ticket and they did not have an agent inside the secure area so I had to leave and reenter. It was a very fast and easy process.