| Nothing.
Actually except for the equalization currents (equalizing the state of charge between both batteries; it is matter of dimensioning the connections for that), it is safer for than the plain series connection. The thing is, parallel connection requires just the number of series cells and their chemistry to be equal. There is no limitation on the capacity each battery has, on its state of aging,...
But you get stuck with lower voltage system, where the wiring resistance makes more trouble. But once you have certain voltage system using lead acid, boosting the battery capacity by adding more of the batteries in parallel is perfectly OK (assuming no system component relies on limited battery capacity to actually prevent its thermal overload, like it is the case for most consumer grade UPSes).
The thing is, the parallel connection keeps the individual batteries perfectly balanced against each other.
On the contrary, using series connection is way more demanding on cell capacity characteristics matching and cell balancing, but offers more convenient (for higher power) higher voltage output.
Big battery shops charge the batteries exactly this way: There are thick copper bus bars runing along the charging desk with a powerful accurately regulated power source feeding them and the individual batteries are connected to it by a clamp cables and left for about a day. or so. The charging current uses to be large initially, but before anything happens the battery gets charged so it reduces itself, till the charging stops completely.
Electrically equivalent is charging system in all cars: The alternator is a 100..200A capable charger, feeding this current into whatever battery a typical car uses (60Ah,...). Only the most modern cars have the charging current regulated more accurately (but there the aim is to accelerate the "last 20%" charge by allowing the voltage to go higher, so the currents stay that high longer).
It is even OK to paralle connect sealed NiMH cells, but there is a caveat: The cells connected in paralle should be thermally well tied to each other. The reason is the charging reaction being exothermic and discharging endothermic (and overcharging onbviously very exothermic), so together with naturally negative temperature coefficient of a cell voltage (common property of any electrochemical system) may form the tendency of the hotter cell to suck in charge from the parallel connected colder cells, mainly when the hotter cell becomes overcharged (slight overcharging is a common way to balance series cells except Li based chemistries). Once the thermal bond between cell is strong enough, it can prevent this.
But this problem is only for NiMH and to a bit less extend NiCd. And a special cell construction, theramlly separating places for H2+O2->water recuperation from the cell structure itself (Toyota uses this in their hybrids on NiMHs - the water recuperation is on top of a cell box, with cooling system attached to it), means the heat from the overcharging does not warm up the cell, so does not cause the voltage to drop at the end of charge, greatly reducing the damaging thermal stress on the cells and greatly simplifying the battery management (no need for individual cell temperature sensors; important to consider, when you need 3x as much cells for the same voltage compare to modern Li based chemistries).
For LiIon, cells are normally connected in parallel, only these groups are connected in series afterwards. The reason is, LiIons can not be balanced by overcharging (as that tends to trigger thermal runaway with a fire and even an explosion as a result), so need active balancer circuits. And by connecting multiple cells in parallel you made these balanced inherently and then need just one common balancer channel for the complete battery.
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