It doesn't seem like it would, but some folks I know are adamant about boiling their water before ingesting it and the online articles I've found on this seem very subjective.
What do you mean by "safer"? If the water is pure to start, there's no point in boiling it. For mildly contaminated water, chlorination is inexpensive, but can form some toxic halogenated carbon compounds. Boiling is very energy intensive, and may require use of fossil fuels (unless you use a solar water heater). Both eliminate most microorganisms, though there are a few, mostly nonpathogenic ones, such as Deinococcus radioduran and others found at undersea volcanic vents, that can survive radiation, heat and other chemicals. Bacteria have even been found living in the common biocide, povidone-iodine! See this source for more information on biocides.
Better alternatives might be ultraviolet sterilization or ozonation.
Boiling water will kill potentially dangerous microorganisms, such as the cholera bacterium.
Filtration is not a clear term when used together with water. It could mean anything from getting some macroscopic debris out to a bacteria-withholding microfilter. The most common usages would probably be said microfilter and the filters common in most areas of Germany which reduce water hardness. While the former may be safe, the latter isn’t. Without more information on the filtering technique, we cannot say whether it is safe or not.
Chlorination will pretty reproducibly kill each and every microorganism. However, it cannot destroy all toxic compounds and not do anything with respect to toxic heavy metals.
Boiling water will also pretty reproducibly kill all microorganisms that have been known to populate human water supplies. Yes T. aquaticus etc. etc, but I don’t think that they will ever get the chance to enter our pipes. It may also destroy some toxic chemicals, but less. And it also cannot do anything with respect to toxic heavy metals.
So boiling water is not safer than chlorination, but it isn’t really less safe either. (If you have chemicals in there that survive chlorination or boiling, you have a very serious problem anyway and probably shouldn’t even shower in the water.) However, boiling has a significant advantage, because chlorine residues in water taste bad.