Hi - the basic answer is that it depends! In particular, it depends on both actual experience to date and the basis on which the prospective reserve is valued.
Let's assume that we are talking about conventional without-profits business, which is what the chapter on surrender values considers (assuming that is the area which has raised this question for you).
The asset share depends on actual experience to date. If this has been poor (eg high expenses, low investment returns) the asset share will be low and may be lower than a prospective reserve. However, if actual experience to date has been good (eg low expenses, high investment returns) then the asset share may be higher than a prospective reserve.
The prospective reserve will depend on the assumptions used in the valuation. If these are best estimate, the prospective reserve might be quite low - and thus more likely to be lower than the asset share. If the assumptions used contain significant margins (eg as would be the case if they were in line with a pricing basis wherein the margins represent the profit loadings) then the prospective reserve might be quite high - and thus more likely to be higher than the asset share.
So the overall comparison depends on both the actual experience achieved to date and the prospective valuation basis used.
If actual experience has been in line with the original premium basis (with profit loadings = margins, as above) and the prospective valuation is performed on the same basis, the two amounts will be the same. This is explored in Q2 of the April 2015 ST2 exam, which also goes on to consider the impact of actual experience differing - so you might find it helpful.
See also Chapter 21 Section 5.2 (including the graphs), which considers the comparison between the two measures in the context of setting surrender values.
Hope that gives you enough to help you with this issue.