Going from a 60 to a 70 profile in the same tyre ie 208 to 208, Evo to Evo will slow the turn in down, this can be compensated for by starting the turn slightly earlier.
Going from a 60 profile road orientated tyre to a 70 profile track orientated Tyre Should feel similar if not a little better.
This is why 012ss, Supercorsas, Rennesports etc dont come in 60 profile, because the tyre profile is more egg shape than a constant round curve, thus meaning a 60 profile in this shape would have virtualy no sidewall.
Benefits of these tyres are the larger footprint offered when leant over aswell as the compound being more favourable for a higher grip level.
Experiencing a slowing of the steering with these sorts of tyre suggest two possibilities either the rider is not putting enough input into turning the bike or the rear ride height is low.