No, this isn't right, at least in the US.
In most cases, all carrier antennas are on the same rack. So if Verizon is on the top rack of the tower, then ALL of Verizon's gear is on that top rack, so the height is the same. There are certain towers, specifically the "stealth" ones made to look like ridiculously huge flag poles, where that's not the case, but the vast majority of cases do have the antennas at the same height. In many cases, the same antennas are being used for 3G and LTE, and sometimes also for 5G-NR.
Separately, the frequencies in use are very similar. Verizon uses 850 MHz CLR spectrum for CDMA/EVDO, and is using 700 MHz upper-C block spectrum for LTE (along with other higher bands). 700 and 850 are similar spectrum with similar reach.
Other carriers are similar. AT&T uses 850 MHz or 1900 MHz for UMTS, while using 700 MHz lower-B and C blocks for LTE (along with other higher bands). T-Mobile runs GSM on PCS (1900 MHz) and/or AWS (2100 MHz) along side LTE on 600 MHz spectrum and, in many places, 700 MHz lower-A block spectrum, which actually should have better range than PCS/AWS. In the area I'm most familiar with, US Cellular has CDMA and LTE on the same 850 MHz CLR spectrum on the same rack of equipment. Range should theoretically be the same, but it is not.
CDMA, which is 2G rather than 3G, did have excellent range. I could make a call on it, albeit somewhat broken up, at -104 dBm; LTE wouldn't even connect until that signal level came up another 15 dB. I can't speak to GSM or UMTS.