Thing - haha! For me the biggest difference was reaching for the trim wheel without looking and not finding it... (old habbits eh?) It was even more confusing where to find the trim when I flew an older PA28 with the trim overhead!!
The only reason I mentioned checklist - and this specifically relates to the fact that he/she is changing school, and the school's checklist may be slightly different. Same applies re: handling notes, this is again only to minimise the potential for the school to milk it a little more... This is only for familiarity. If you've read it a few times, in the order and style that the particular checklist they use has, it makes it a little easier once you're in the plane.
Generally speaking, all SEP planes can be flown with the same "patter", (ie: downwind checks that I was taught included "gear - fixed, propeller pitch fixed... etc... which I have used in all SEPs I have flown without alteration other than the particular answer to each, for instance "gear down and locked, three greens" or "carb-heat - not applicable" or "alternator not present") aside from the slightly different engine start procedures - its all the same titles.
Re: gear issue, I think it would be wise, to know your systems. I have always gone through the first "sanity" check before reaching for the checklist (ie: in the PA28 - are my instrument lights on in daylight? Have I selected gear down? Is the knob really in the down position? Are the light bulbs working? Is the emergency gear lever in the correct position? Is the override on? - then when all those failed, I placed myself in a known position, away from the circuit and planned a loose holding pattern to work out my issues, and then and only then reached for the checklist to work through it methodically to ensure all possibilities are covered, before making the decision where I would rather land her on the belly, ie: which aerodromes nearby with emergency facilities open? tarmac? grass? etc...
Generally - something in the sanity check will remind you that you've been an idiot, and you can rectify this without having to leave the circuit to work out the problem by following a checklist properly.
Yes, Cessna_79S - I think the move between C150 and C172 will be similar to moving from say... a Nissan Micra to a Ford Focus - the controls are the same, the same principles apply when you're driving, its a bit bigger, have a bigger engine, the speeds between the gears is a little different, as is where all the buttons are. But really... Its pretty much the same - you should get it pretty instantly. The reason I mention a few hours, is that generally schools will milk it if they can, and a low hour PPL they'll find something that they believe you weren't taught in the same way and try to persuade you their technique is better.... (been there many times). Clubs are a much better option in my mind!