How to connect 2 different power supplies together
The answer is probably yes, you should connect them together.  If the old supply was not isolated, and you replace it with two non-isolated supplies, then the grounds will be connected together anyway through the supply ground.  If the old supply was isolated, you need to replace it with isolated supplies and connect the grounds together.

Make sure the supplies are fully compatible, it's not just a case of having the right voltage. Make sure the isolation is the same or better, the maximum current on each rail is the same or larger, the minimum current for stability is the same or smaller etc.