A study by Goto et al in 2005 examined exactly this with a 30 seconds break!
They found that performing the sets with no break caused greater increase in strength, muscular endurance and particular in hypertrophy than performing with breaks.
Muscle growth was found to be 12.9 % in the no break group and 4% in the break group.
Further they measured increased growth hormone response and metabolic stress (lactate) in the no break group.
It seems the last reps before failure matters the most at least for hypertrophy: effective reps.
However these last reps also causes the most recovery time, so this has to be balanced. I suggest stopping 1-2 reps short of failure, except maybe for the last set.
Sets of 10 causes hypertrophy trough metabolic stress which is the accumulation over time during a set of byproducts of energy production in the muscle cells.
These byproducts causes hormonal signals that stimulate the energy supply part of the muscle cells, the mitochondrion, to grow.
By breaking the set into two you are negating this mechanism since the metabolic stress is reset by the breaks in between the sets.
Less metabolic stress equals less hormonal signals, equals less muscle growth, ie. less hypertrophy.
If you can lift a weight for 10 reps that weight is only 75% of your 1 RM.
Muscle fibers are grouped together in motor units. There is a great variety in the number of muscle fibers controlled by each motor unit.
A small motor unit controls only a few muscle fibers whereas a large motor unit controls thousands of muscle fibers.
Fast-twitch muscle fibers are controlled by the largest motor units.
A motor unit either contract (on) or not (off). There is no controllable gradual force output from each motor unit.
According to the size principle the motor units are recruited in an orderly fashion from small to large.
When you do the first rep of your 10 rep set there is 25 % of strength not being used. This corresponds to a few motor units controlling fast-twitch muscle fibers.
Sadly when you do the first rep of your next set the same thing happens. These same motor units are not contracting.
And in order for a muscle fiber to get stronger it must be trained.
However as your set progresses the muscle fibers that are contracting starts to fatigue (possibly due to the metabolic stress).
They still keep contracting but their force output is reduced. In order to maintain the total force output more motor units are recruited.
Finally after 10 reps all motor units are recruited but their force output is so reduced that the required total force can not be met,
and you fail to make another rep.
When you break a set of 10 reps after 5 reps there are motor units not being trained and it is the same motor units every time, and they control fast-twitch muscle fibers.
One benefit of breaking the sets is that recovery time is reduced.
Some very experienced powerlifters that are already close to maxed out at underlying strength use this to almost double their number of workouts.
Thereby they achieve a greater amount of training of the neural efficiency.
This is the called the Bulgarian method or more recently the Norwegian method ;-).
Recruiting the fast-twitch muscle fibers trough fatigue is neurally different from recruiting them voluntarily from first rep.
Therefore I think alternating between hypertrophy and max strength training may be useful.
Goto et al: The Impact of Metabolic Stress on Hormonal Responses and Muscular Adaptations
Jeff Nippard: Effective Reps
The short and sweet Borge Fagerli guide to getting bigger and stronger
Beardsley: How many stimulating reps are there in each set to failure?
Greg Nuckols: The Evidence is Lacking for