It's partly a question of who does the QoS. You or the carrier. QoS is about managing congestion. When packets are going to get dropped, you want to be able to choose which packets they are.
In a point to point network, you're in control. The congestion problems are going to occur on your routers. You (for example) have a high speed Ethernet coming into your router and you need to funnel it down a narrow pipe to your carrier. But the carrier is not going to be dropping anything once it gets into the pipe. So you apply a QoS policy on your router(s) and you're done.
[If the carrier is delivering a virtual point to point circuit and their underlying network is congested, this ideal scenario may not apply and the carrier may still be dropping your frames].
In a meshed network, you're not in control. You still have congestion possibilities at your edge routers where you choke down from an Ethernet LAN to the carrier's tail circuit at the source site and you still have to deal with those issues yourself. But in addition you now have the problem that many of your sites may be sourcing traffic directed to a single destination site, overloading that site's tail circuit. The carrier has to decide what traffic gets dropped at that choke point.
So if you're putting together a fully meshed MPLS network, it's important to know how the carrier can support your QoS policy on their equipment. In general, you tag the frames and the carrier applies the policy. Depending on the carrier there may be restrictions on the tags they support and the policies they can implement for you.
MPLS access links would normally use a point to point circuit anyway.
MPLS proper is the "cloud" bit operated by the carrier
in most setups the label switching bit is only within the carrier core network, and will not go as far as a customer site - so they could be plugging all those access links into a central router instead....
some services do - it sounds like you are referring to a L3 VPN over MPLS.
But some MPLS services across are point to point - Ethernet L2 circuit emulation is common.
The access links to / from a customer site run IP, so no difference.
The MPLS core QoS field inside a label is only 3 bits, so the "native" per packet QoS is less rich than say DSCP.
Since the backbone tends to be much faster than customer access links that may not matter (as if you never have packets building up in a Q there is not much QoS can do to re-order traffic).
Some MPLS backbones dont do any QoS handling in the core, but just at the PE router where customer links meet the high bandwidth bit, since it is sometimes simpler and easier for the carrier to throw bandwidth at the problem