>>My question is this, besides the OBi202 having the ability of 2 phone lines, is the connection quality and control from the OBi200 and the OBi202 to the modem the same?
Yes and no. The OBi200 Series Internet port is 100Mbps Ethernet; but in Router Mode, the OBi202 throughput is 30Mbps max.
>>Is the function of the QOS on the OBi202 only to manage the data transfer of a device connected through its extra LAN port?
Yes, it is to insure sufficient bandwidth for VoIP traffic in Router Mode, in case you are routing too much LAN traffic through that 30Mbps max bottleneck via the OBi LAN port.
>>Or, does the QOS on the OBi202 make a qualitative difference over the OBi200 when connected from the OBi device directly to the modem?
If the OBi202 is your router, its QoS can preserve bandwidth for the VoIP traffic. Otherwise, a more capable site router could do the same thing.
I would not buy the OBi202 for its router or QoS features. A niche application might have use for these, but I would buy it for its second PHONE port and run it in Bridge Mode as a 3-port 100Mbps Ethernet switch. And use a more capable site router with greater features.