The saucers may have looked similar, but the NX-01 was cramped inside. All of the technology might have looked more advanced, but was indeed less sophisticated than TOS. You have to understand that TOS is a product of it's time. They're not going to make any of these shows look like the bridge is made from boxes and flashing lights. Yes they did it on Enterprise during the mirror universe episode and although it was neat, it still looked dated.
As for the phasers, they were phase cannons which are different. Look them up in Memory Alpha online. There's a lot of variance on phasers, pulse cannons and pulse phase cannons even through TOS and it's movies let alone the other series. There's also a difference between the NX-01 photonic torpedo and a photon torpedo which again can be looked up on Memory Alpha online.
Human made transporters were invented in 2121 and the first operable transporter was developed before 2139. Since the NX-01 was launched in 2152 I don't see why it wouldn't have a transporter. They even said it was cleared for bio transport and none of the crew had ever done it prior to being on the NX-01. Again all of this is in Memory Alpha online.
The Shenzhou in the Discovery trailer looks like an advanced NX ship and could be older than we think. I'm hoping it is and that the Discovery and it's technology will mimic, but not replicate the TOS era. Enterprise is very much indeed cannon and even though there might be a couple hiccups, it's in the prime timeline.