As far as I can tell you've got two main reasons here why TC in it's "base" configuration will differ from Ubuntu:
(1) The 'tput' command is not included in the Core initrd, but would be available via the 'ncurses-utils.tcz' extension, and
(2) the prompting escape codes '\d' and '\t' are not supported by the default shell (i.e. BusyBox 'ash', which at least supports '\u', '\w', and '\$'). The missing ones would become available if you'd change your shell with the help of the 'bash.tcz' extension.
So installation of two extensions (plus a change of your default shell in '/etc/passwd') would allow you to use the 'PS1' setting from Ubuntu in an unchanged fashion.
EDIT: I've now come up with a way to express '\d' and '\t' even in 'ash': by replacing \d \t with $(date "+%a %b %d %T") the requirement to install 'bash' is gone. Furthermore I've used in my testing just some of the colors which are already defined in '/etc/init.d/tc-functions' so with
export PS1='${RED}(${YELLOW}$(date "+%a %b %d %T")${RED}):[${GREEN}\u${RED}:${GREEN}\w${RED}]\$${NORMAL}>- '
I managed to produce a prompt not too dissimilar to the original version. So I don't see a problem to also "ditch" the requirement for the 'ncurses-utils.tcz' extension.
IMHO the whole prompt looks pretty "sick", but as we know "Beauty is in the eye of the beholder" ...