There is no real general answer to this as the drive and handling characteristics will vary from vehicle to vehicle, depending particularly on weight distribution and suspension design.
However the effect of weight transfer tends to be more significant under braking than acceleration as most cars are capable of generating higher braking loads than acceleration.
There are also some very important advantages to FWD cars
- Because there is no prop shaft to take drive to the rear you save space in the cabin. This goes hand in hand with a transverse engine layout (a logical consequence of FWD) and is a big factor in making cars more compact overall and with more usable internal space.
- FWD lends itself well to designing vehicles around a general purpose modular floor-pan. This allows manufacturers to make a lot of different models around one set of running gear and floor (a bit like a truck ladder chassis). While preserving the advantages of monocoque construction.
- For general everyday driving the handling of a FWD is generally safer as loss of grip through under-steer tends to me more progressive than overseer through loss of traction at the rear wheels and easier to correct as well as less likely to provoke a dangerously inappropriate reaction in an inexperienced driver.
- Driven steering wheels can improve handling in certain types of corner as the drive is pulling the vehicle in the desired direction as opposed to RWD which is acting at some tangent to the steering direction.
- Having the engine weight over the drive wheels improves traction in general driving, especially in slippery conditions. FWD cars generally handle better in snow, ice and mud.
RWD is generally only an advantage in cars with a very high power to weight ratio, especially mid engined cars where weight distribution is not biased towards the front. The main reason for this is that when cars are expected to handle steering and traction/braking loads simultaneously.
It is also worth noting that this only really matters in driving conditions where tyres are approaching the limit of grip eg in racing which is not what the majority of production cars are designed for.
Also bear in mind that up untill the point where the drive wheels actually lose traction/grip it make no difference and this is generally a lot more manageable (especially for non-expert drivers) in a FWD car where you just don't accelerate quite as quickly as opposed to a RWD car where it can end up swapping ends.
In summary for the vast majority of consumer cars FWD is just plain better and there are plenty of fairly large cars with pretty decent performance which are FWD.
Once you get into the realms of out and out sports cars things are a bit different but then again most proper sports cars are mid-engined in any case (note also that most 'front engined' performance cars have the mass of the engine well behind the front axle.
If anything the trend has been for larger and more powerful card to be FWD as time has gone on.
It is also worth noting that the Mini, one of the first mass produced FWD cars was extremely successful in rallying in the 1960s.