First, let's describe the two hypotheses and then analyze for a conclusion.
The Unitary System Hypothesis is quite interesting. It stems from the continuous debate on whether dual-language babies acquire one or two languages at the same time. The essential question posted in the debate is whether the babies realize that they are speaking two languages, or whether their brain acquire both languages as one same unit which they will begin to differentiate at around age three when their speech formation begins. In all, the USH basically supports the claim that children learn ONE language first, and the second later at a different rate, and NOT simultaneously.
The argument in favor of the USH is that studies made with children of dual language homes, at age two and three, show evidence of code-switching. Code-switching suggests that the child knows both languages (switching) but uses one language more than the other. Other studies suggest that the reason for the rate of usage of L1 and L2 is entirely dependant on input, and that such input is found to be imbalanced in most families. This means one thing: that USH's claim of the acquisition of one language at a time depends on how much the parents expose the children to the languages; one lexicon, one grammar. The implication for learners is that the parents must be consistent in speaking both languages at the same rate at home, or they will find the child opting for the common language of the home and then code-switching with the second one.
The Separate Systems Hypothesis (SSH) is the opposite to USH. In this hypothesis, the argument is that the child will build two separate lexicons, and two separate grammars for each language. The SSH and USH look quite similar in that, at some point, the child will indeed use both languages in their particular forms differently. If consistent input is given, the child will eventually develop two completely languages correctly. They key is input, consistency, and appropriate usage of both language groups.
Remember that L2 research is based on theory, and not on scientific discovery that could lead us to a factual source of language acquisition. Hence, both theories do intermingle, yet, they both agree in that parents must take their language usage at home seriously and not tend to favor one language over another. This is the only way to succeed in an L1/L2 home