If you use a landline (a twirled wire coming into your home from the power pole), indeed the 'last mile' is owned by the same company. At the local switch, a number of telecom providers then connect with ma-bells hardwired connection into your home. Those telecom providers (e.g. broadview) will then lease out that connection to a multitude of providers including VOIP outfits like vonage or magic-jack. So if your problem is indeed related to that 'last mile' wiring between your house and the local office, you are not going to gain anything by switching providers. If the problems are above that (and they often are), changing providers will change things.
DSLs structures basically follow the phone layout with only one provider owning the wire into your house, 3 or 4 providers at the level of the local switch and a bunch of re-sellers that piggyback on those existing connections.
If you have a stable internet connection, you can use VoIP. In that case, the modem in your house converts the voice into a data stream that then uses your internet connection to travel to the central server run by your VoIP provider. From there, it then gets routed back via the telecom network to your local switch to be fed back into the network somewhere local to you (so phonecalls made to your local number show up as local tolling calls). So with VoIP your local phonecall will probably make a round-trip to Kansas City or LA before it goes 3 houses over.
Used to have Verizon business and nothing ever worked. Then used a number of Vonage boxes (terminal adaptors in telcom lingo) for a couple of years. Now I have switched to a multi-line business system from a company called Nuvio that uses actual VoIP phones and something called a 'hosted PBX'. The advantage of using that setup is that if the internet connection goes down, the customers dont get a 'this line is disconnected' or 'call cannot be completed as dialed' but rather they talk to our auto-attendant and the calls can be re-routed to cellphones or other land lines.