The 2 year condition probably relates to the time needed before you could apply for internal promotions i.e. promotion competitions limited to those already in the system.
External competitions by contrast are open to everyone and so you can continue to apply for these even if you’ve only recently accepted a position.
In terms of preference, the agencies are generally more specialist and can offer more attractive terms than the Civil Service of HSE. They may be more limited however in terms of scope for promotion and mobility.
The CS has a better reputation than the HSE in terms of a place to work. There is good opportunity for mobility between government departments within the CS structure but no mobility between the CS and HSE.
In both the CS and HSE, the grades are more generalist (EO, HEO etc) although you are likely to put into a role (e.g. a policy area) that will require you to develop specialist knowledge.
Given the choice of the CS and the HSE, the CS is probably a more progressive long term choice.