I had a longer conversation with my bro-in-law to try to get more information.
The modulus of elasticity determines how much deformation occurs in a material with a given load in the elastic region. The elastic region is defined as the range of loads starting from 0 to the point where the load becomes high enough to cause permanent deformation. With that said, the modulus of elasticity of asphalt in compression (which is the state it's in while you're running on it) is 0.2 ksi. 1 ksi = 1000 lbs per sq. in. The modulus of elasticity of concrete is 3 ksi. That means a load that causes a deformation of x on concrete will cause a deformation of 15x on asphalt.
Some math:
I previously calculated that a 200 lb human could put as much as 100 psi (rounded down for a whole number) on his foot at the moment of impact. A shoe probably reduces that by a factor of 4 (I failed to mention this earlier) because of the distributed load due to the sole of the shoe. So, a 200 lb person could put 25 psi of pressure on an asphalt road. That's 12.5% of the modulus of elasticity, meaning if the asphalt is 2" thick, it will compress 0.25" very briefly. Concrete would compress by 0.016". Even if the pressures are off by a factor of 3, asphalt would still compress noticeably more than concrete. My shoe compresses about 0.4", so an asphalt road compressing by even 0.05" would be noticeable (12.5%).
Those are peak numbers. Reduce the pressure exerted by the same person by 50%, which is more realistic for long distance running (force per step = body weight * 1.75 (instead of 3.5 like I used earlier)). Now the asphalt compression is roughly 6%. Changing the thickness of the asphalt, compression of the shoe, weight of the runner, and several other things will obviously affect the results. It may turn out to be less than 1% in some cases, so I doubt a person in that situation would be able to feel the difference. However, it could end up being close to 10% in other situations and I strongly believe a person can feel that. Note: this is all at 25C. The modulus of elasticity decreases as temperature increases, so on a hot day the asphalt will be weaker while concrete stays essentially constant at all survivable ambient temperatures.
As it turns out, my previous comments about asphalt returning the same amount of energy were incorrect. It should definitely return less as it absorbs much more than concrete. I read some of that on my own, but I trust this new information much more as it came from someone who I trust is an expert in this field.