A remap will get you more power, but keep in mind that the vehicle isn't designed to take more power (it should be OK), so things like the gearbox won't last so long.
The SD4 engine produces the same maximum torque as the TD4, but has a higher fuel delivery at higher RPMs, so makes a few extra BHP at the top end. The SD4 also has a turbo designed for the higher heat generated by the extra fuel, which the TD4 doesn't need, so the turbo life could well be reduced.
When driving, there isn't really much difference between a correctly running TD4 and an SD4. The SD4 has a better throttle response, but unless the RPM is taken able 3500, then it doesn't actually produce much more actually power.
But a good remap will optimise a TD4, so making it much more SD4 like, with the potential issues previously stated.
If it's before 2010, then make sure your TD4 is not down on compression in 1 or more cylinders, caused by dropped swirl flap damage.
Also before spending money on frivolities, it's very sensible to have all the fluids in the gearbox and AWD system changed (PTU, rear diff and Haldex) as those units all fail, likely due to stupidity long fluid change interval.
Re tyres, yes ATs will fit the standard wheels, but what size wheels you have will determine what AT tyres are available. I'd go for Yokohama Geolander AT 015, and will do on my FL2 when my current tyres need changing. The Geolander AT 015 give superior grip in all conditions, including wet tarmac, which is where many AT tyres fall well short of standard road tyres.
