GPRS Tunneling protocol has multiple variants such as GTPv1-C, GTPv1-U, GTPv2-C. If you look into GTPv1-C and GTPv2-C header then you can easily make out the difference and why GTPv2-C is being used for LTE signalling among MME, SGW and PGW . One major difference what I found GTPv2-C can piggyback multiple messages but GTPv1-C does not have support of piggybacking. However there was no requirement on change of GTPv1-U so it is being used in LTE as it is.
References
Spec 29.060
Spec 29.281
Spec 29.274
https://en.wikipedia.org/wiki/GPRS_Tunnelling_Protocol