L/360 does not define the 9 1/2" joist selected; you need to tell us the I-Joist model number (210 or 230).

The issue here is floor bounce which is not addressed by code, manufacturer or acceptable engineering practice; it is determined solely by the experience of the designer.

If you intend to use a 9 1/2" I-Joist, I recommend using the strongest one which is model 230. Its Live Load deflection is greater than L/480 which is about 3/8" at the center of the 16 ft joist.

No one can say for sure if that is stiff enough to satisfy your family but it will be a lot better than one of the other models.

To increase the floor stiffness you would need to use an 11 7/8" deep I-Joist or space the smaller ones closer together. You might want to ask your builder why the joists were taller in the first place. The only reason I can think of is to limit floor bounce.

If you want tile on the second floor anywhere, you need the heavier duty and thicker ones. Also, if you are going to be running ductwork between them, the deeper ones will be better for the trunk lines carrying the majority of the HVAC upstairs. The only reason I can think of to use the smaller ones is to save some money and it's a penny wise pound foolish savings.

There's a few things to consider when selecting joist depth, and Live_Wire and Renovator have mentioned most of it.
Definitely talk to your GC about fitting HVAC ducts for 9.5â joist depth, and bulkheads locations if any.
Renovator8 made a good point on TJI classes 210,230, 360 and 560.
The 9.5â joist with 1330 lbs shear can be grade 210 or 230, both with almost the same deflection stiffness at 186 or 206 EI.
The 11.875â joist with 1705 lbs shear, that you compared with, is grade 360 with a deflection stiffness of 419 EI.

Comparing the two, 11.875â TJI360 doubles the stiffness for the 9.5â TJI230, therefore given you 50% less deflection.
You could run 9.5â joist @ 12â instead of 16â to give you a stiffer floor as well,

I would suggest that you ask your GC to supply you with the calculations for both of the joist, and compare the values. As Renovator8 mentioned, Live load deflection of L/360 is acceptable, and L/480 is better. Check the loadings in the calculation that should reflect your actual need. The floor span table on pg4 of the PDF gives you a rough idea of what joist size you need.

Ren8, L360 is the 11" joist. The builder has not specified which 9" one we would use; I presume the heaviest.

We do have laundry on the second floor, but I guess that's more of a constant vibration, not something which would cause a lot of bounce?

The reason I'm considering this is to give us more room in our entry. If I have to do the height between floors with the 11" i-joist, then would have a 109" floor to floor distance. For this, I need 15 rises/14 treads on the stairs (14 rises would give me 7.79", too tall for the code's max of 7.75"). Using Ren8's formula, 15 rises and 14 treads should be R=7.26R T=10.3, leaving only 3'8" between the front door and the stairs. If I could have a 107" floor to floor, I could do 14 rises/13 treads, R=7.64 T=10, with a 14" shorter running, leaving 5' between the front door and stairs.

I can push the stairs back without making upstairs bedrooms smaller (they are already at a minimum). While the 3'8 isn't the end of the world, the 5' entry sure would be nice, which is why I'm trying to get a handle on the difference between the i-joists. I really have no idea which is appropriate, and I don't know how I would decide unless I could find similar houses with each joist, obviously not really a possibility. Thanks for the thoughts.

Here is a link that might be useful: Link with floor plans (stair rise/run shown is not ideal)

Floor bounce is the sense that the floor is shaking when you or someone else walks across it. Some people are very sensitive to it and others don't seem to care.

In addition to that variable there is no way to calculate the degree of bounce. The maximum deflection at the full design loading is only a very rough indicator of bounce. One approach is to select a reasonable joist according to accepted engineering design standards, the code tables, or a manufacturer's chart and then upgrade to the next larger size or the next smaller spacing.

For the I-Joists your contractor is using that would mean selecting a TJI 230 but the deflection difference is not very great. Another approach is to design for a span that is 20% longer.