Question: Sorry if I haven't worded the title very well, feel free to improve.

Let me explain before I ask my question...

We have purchased a [car carrier](https://www.petbarn.com.au/playmate-airline-spec-open-top-pet-carrier-white-grey-medium) (small version) for our dog and also purchased [some straps](https://rads.stackoverflow.com/amzn/click/com/B005SH05E6) to secure it to the seat; however we have noticed that even though it is secured to the seatbelt it is still a little loose (you can move the carrier forward a bit before it attempts to prevent further movement).

I have heard someone else that has used these same straps state they have instead put the straps around the whole back of the seat rather than use the seatbelt and they have stated it is now much more secure/tighter against the seat and hence prevents much movement.

So my question is - which method is better/safer?

* Securing it around the seat, to me, *seems* like it may be a better option as it helps prevent movement, but I'm wondering, because of this lack of movement, would our dog now have to sustain more **g-force**?
* Securing it to the seatbelt, to me, would seem to propel the carrier forward on an impact until it is stopped and then our dog would be thrown forward into the front of the carrier in a more "jerky" fashion then when secure but *may* not have to sustain as much g-force!?

As a side note, if it matters, we have been told by [CPS](https://www.centerforpetsafety.org/) that the straps we purchased are **not** *strength rated*; which I assume means they have the potential to break at high points of impact, but we are open to purchasing better ones if need be, but I am also cautious about using straps not specifically made for carriers as I have heard using seatbelts around carriers [can potentially crush them](https://www.youtube.com/watch?v=YnES6NIMHsM).

Answer: 
The short answer to the question as posed in the title to your post is both.

The purpose of the seatbelt is to restrain you so that you stop with the car thereby making your stopping distance the same as the car and greater than if you had no seatbelt. Without the seat belt your inertia keeps you moving forward at the same velocity until you impact an object in the car which then stops you. You are then at the mercy of how much "give" the object has since that will determine your stopping distance. 

A crash which stops the car and driver must take away all its kinetic energy according to the work energy principle which states that the net work done on an object equals its change in kinetic energy, or 

$$F\_{ave}d=-\frac{mv^2}{2}$$

Where $F\_{ave}$ = the average force you experience.

$d$ = your (and the vehicles) stopping distance.

$m$ = your mass

$v$ = your (and vehicle) relative velocity with wall before the crash

The vehicles crumple zone, seat belts, and air bags are all designed to increase your stopping distance and/or absorb the energy of the impact.

On the other hand, seat belts with a moderate amount of stretch further increases the stopping distance of the occupant, additionally reducing the average force experienced by the occupant while still restraining the occupant from impacting the objects within the vehicle.

Hope this helps.
I refer you Bob D's answer above for the physics.

At the moment of impact, the carrier will move forward until it reaches the limit of the restraining straps. The straps then undergo a deformation (elastic and inelastic), over the scale of a few centimetres, that decelerates the load. This process is the same whether the straps are loose or tight because the load is moving at the same speed at the moment when they reach their limit and begin to bite.

So it doesn't really matter if the straps are very tight or not. As long as they not so slack that the carrier can move forward enough to impact something in front.