how does the AMG Project 1 and the Aston Martin Valkyrie compare to GT3 cars?
the claimed downforce of the Valkyrie is 4000lb and it weights a bit over 2200lb (1 metric ton) while it has a rumoured power to eclipse 1 to 1 hp/kg
@Matski provided a very well constructed and informative post about how a GT3 race car or any race car in general compares to the road going hypercars. Tyres play a critical role in performance, and the P15 is equipped with a set of Pirelli Trofeo R, and I believe that no matter how much grip it can generate, it won't match the level of a slick racing one. McLaren didn't mention that the P15 Senna is faster than a GT3 car, because this is a very bold claim, and if it's true, the press release will mention such information at least 4 times.
Another example on the effect of tyres can be seen from the Sachsenring once again:
Road car: 1:26.77 / Porsche 918 Spyder / Auto Bild
Race car: 1:26.73 / VW Golf GTI TCR / ADAC TCR Masters 2017 Qualifying
The Golf GTI TCR has around 350 HP and weighs around 1250 KG. Both figures are subject to change due to BoP. According to VW, the TCR version can do the 0-100 KPH in 5.2 seconds.
Race cars are truly built to a single purpose, which is to go around a racing circuit as fast as possible within the regulations. A road going supercar, no matter how power it generates, or the amount of the downforce it's supposed to produce, isn't optimized for a single purpose, because it is built to do a second function, which is being used on the street.
Regarding your question about the Aston Martin Valkyrie and the Mercedes-AMG Project one, it's not logical in my humble opinion to compare them to a GT3 racer due to several reasons. First of all, the two cars you mentioned are purpose built prototypes that didn't go through any sort of performance test as of yet. Their configuration is completely different to the standard GT racer, because they were built from the ground up to have a bespoke chassis, and were optimized to achieve a specific aerodynamic / handling target.
A GT car (GTE/GT3/GT4/TCR/NGTC/etc...) starts its life by using the bodyshell of its road going counterpart, then the engineers start to build the car depending on the regulations that govern each category.
Here is another very good post by
@Matski that explains GT racing cars from a DTM thread:
DTM 2017 season
I've taken a look the press release of the AMG and the Aston, and couldn't find what type of tires will be used* or how much downforce can be generated, so I can't provide a thorough comparison. However, while both of these cars use Formula 1 drivetrains, they remind me of an LMP car. In FIA WEC, an LMP1 car (the fastest category) is about 15~20 seconds quicker than a GTE car, which is about 1.5~2 seconds quicker than the GT3 car, while an LMP2 car is about 9~13 seconds quicker than a GTE car.
I believe due to being specific built, these two may go around the track quicker than a GT3 car around the track IF they are equipped with racing slicks. On street tyres, I would say they'll be slower.
My reasoning is based on comparing another set of lap times, this time for the Ferrari FXX-K (it can be categorized in the same class as the Valkyrie and the Project one, even if its performance is assumed to be on a lower level) and the Ferrari 488 Challenge. Around Fiorano circuit, the FXX-K posted a lap time of 1:14.00, while the 488 Challenge posted a lap time of 1:15.5, assuming that both cars are on slick tyres. The FXX-K produces around 1050 PS, while the Challenge car is a race prepped 488 GTB that is simpler and slower than a GT3 car. This means the GT3 car is quicker than the FXX-K. Moreover, the new FXX-K EVO is said to produce a higher downforce level that is similar to the 488 GTE and the 488 GT3, while being lighter than the FXX-K.
However, I'm not a mechanical engineer, so I could be wrong on what I've said.
Another long post...
* EDIT: The AMG is using Michelin Pilot Sport Cup 2