As I mentioned, having the title may look good on your CV, until it gets to interview and they ask what experience you gained in that role and it turns out to be not much more than in the technician position.
When you say "a potential IT technician" is this for someone to replace your now vacant position?
What does the office network consist of? Are we talking AD with group policy, internal Exchange server etc, or 10 PCs connected to a 16 port switch in a rack?
When you say "will have a say in IT budget and where money should be spent" are you actually given the money and told to get on with it, or just asked for your opinion when whoever's in charge decides to buy new kit?
Sorry for the interrogation, but it just seems rather convenient for them to suddenly realise they need an additional technician and an IT manager when you're leaving, and I'm trying to work out if the new role is going to be what they say it is.
Do this - not because it will decide for you, but because in the few seconds it's in the air, you'll realise which side you want to come up

(horribly misquoted from somewhere!)
I will just back up my suggestions, by stating that I worked as IT support in a college for 4 years, and the experienced I gained there was invaluable, purely because of the huge range of things I worked on - everything from hardware, structured cabling, Cisco networking, AD & group policy, website design, IP telephony, etc. along with soft skills like writing documentation, project management, staff management, etc.