Ring LWE schemes are relatively simple on a computation level -- the large majority of time is spent doing vector multiplication (another significant portion is sampling the error distribution). This is ideal for parallelization. So typically, RLWE implemented using the AVX2 instruction sets are significantly faster (for example, see a 3x speed improvement for one popular RLWE scheme: New Hope). I'm not sure on the ubiquity of AVX2 instructions on mobile devices, perhaps someone else can chime in.
That said, RLWE just isn't very computationally expensive in general. The paper above mentions that in terms of performance, the AVX2 implementation is in "the same ballpark" as state of the art ECDH implementations that use Curve25519 (which is one of the fastest ECC curves). I couldn't immediately find benchmarks comparing the two, and I don't know how to quantify "the same ballpark", but I've never heard anyone complain that RLWE is too costly performance-wise. So I don't think that the mobile CPU is the bottleneck.
Concerning RLWE, people do complain about the bandwidth of the key exchange. Even the best RLWE schemes still require much more data transfer (see the nice chart in the Frodo paper), which can significantly increase latency for poor connections. This appears to be corroborated by the results of Google's post-quantum TLS experiment, CECPQ1.