Well, depends on your setup actually. For those living in high rise buildings, there is no chance at all to use dual phone lines. Once Maxis Fibre Home is installed, the TM line will be pulled out at the exchange point, thus, users will NOT BE ABLE to use that phone number line anymore, and together with that, no more streamyx. For landed, still possible, since it is a seperate new fibre optic line. But do take note that it will take 3-4 weeks for TM to process your cancellation request, thus, almost 1 month of wastage, especially those staying in high rise.

High rise installation here. I can confirm that you can go ahead with whatever you prefer (either terminate first or later).

The moment TM + Maxis guy come and set-up, TM will just go to the connection centre (or whatever it's called) in your building / block, switch your port settings to their unifi / home fiber (HSBA) port.

I realised the TM guy had arrived (Maxis' guy already beside me, I was doing my web development, online) the moment my internet went off with no ADSL signal. (The TM guy just reconfigure/remove/unplug/change setting/i don't really know what he do behind), moments later he came up to configure TM's modem configuration and viola!  I'm activated with high speed fiber.

The only problem is, I think, TM / Maxis did not activate my account and they couldn't get my connection to online, although the DSL signal is there. They just called back to centre to check and few minutes later, everything's done

Sorry for my long post tho, TL;DR version:
Doesn't matter if you terminate now or later, they're gonna replace your existing port with new installation anyway.

Default username & Password for Thomson Router
Username : MaxisBB
Password : <blank> (No characters, leave it blank, just press log-in)
Username : Administrator
Password : <access key on a sticker at the bottom of the router>

Note: Be warned that it is case sensitive

Part of the T&C from Maxis Fiber internet...
6. You accept and acknowledge that Maxis reserves the right to leverage onto your residential WiFi modem to cater to the Maxis Hotspot service which may be accessible by the general public who are subscribed to the service. The Maxis WiFi Hotspot service does not increase your available bandwidth and will not impact your internet quota nor will it cause degradation of the Service performance, security or risk issue

read more , while its true that any internet connection to internet must have a Public IP BUT

the main difference is where is the Public IP located in the network hierarchy.

For normal maxis ftth setup
users are given private IP at their home and kept the public IP at their own server/equipment. In this scenario, for you to reach the Internet, you must pass through their server/equipment. Mind you, this particular public IP could be shared with other maxis ftth to reach the internet. Typically, this type of setup is

1 public IP(maxis data center) -- > many, maxis private IPs (users home router) --> many, your home private IPs(users ipad,phone, notebook, pc)

so, for data communication in the internet others will only be able to see your public IP, once data routed to the public IP, maxis equipment will then have to route it to the appropriate users (private IPs)
For maxis ftth setup with public IP
users are given a public IP (dynamic one of course) at their home directly. So in this case, between you and the internet is just the home router and this public IP is not shared by others at any point in time. Typically, this tpe of setup is

1 public IP(users home router) --> many, your home private IPs (users ipad, phone etc etc)

by using this setup, you have direct control over the the traffic if your router is capable of doing it and of course if you have admin access to it.
Note: In most cases, normal internet activities doesn't really which setup you have, what important is you have a connection and those routers will manage the route appropriately. However for example a cctv setup, you will require certain ports to be forwarded to the local private IP of the cctv equipments, therefor people suggest to get the public IP setup so that you have control over the router. In fact, cctv setups will even work using the normal setup IF Maxis helps you to port forward the necessary ports from the internet to your private IP (However, that might create management mess and most likely there are strict protocols to follow to allow the changes which means they will most likely wont do it for you)

BTW, public IP or private IP have no relation to your LINK speed. Download speed MIGHT be affected though depending the software you use. LINK speed and Download speed is not the same ya.