Similarities :) There are a lot. Seem to me funny explaining this but a doubt can be anything.
Both are defined by 3gpp. Both supports voice call as well as data. Video streaming. In both You can use data as well as voice at a time. Both supports IMS. Both need frequency band, Equipments, Core Network elements, billing records, everything was there in UMTS is also possible in LTE plus some enhanced features.
Again i don't want to go in similarities the thing is UMTS was developed before and came in 3rd generation obviously LTE came from some basics of previous releases. So it is enhanced version. Similarities are all. Whatever UMTS was doing LTE can also do.
Gradually everything has changed.