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First let us try to understand how one differs from the other.
DSL - Digital Subscriber Line... data being transmitted through the existing phone lines
Wimax and LTE being transmitted over the air the difference being Wimax operating at a lower frequency thus theoretically having a wider footprint (than LTE)... imagine a giant wifi zone. LTE operates in higher frequencies and are more integrated into mobile phones and therefore in all probability use the celltowers as their source of transmission and reception. Though speed and bandwidth are theoretically fast, it is still a maturing technology and sites offered by Globe are still very limited and footprints are small.
In theory, DSL should provide you with a more stable and consistent delivery of data regardless of the weather condition as its dependent factor would only be the quality of the physical line.
Wireless technology like LTE and Wimax have other factors that may affect their delivery like weather conditions, topography, indoor reception, propagation of antenna and even the number of users utilizing the technology all at the same time among others.
Ultimately, it would have to boil down to which service is available and better utilized in your specific area.